Stand by Me Help, Heterogeneity and Commitment in Experimental Coordination Games

by JORDI BRANDTS* , DAVID J. COOPER** AND ENRIQUE FATAS

March 10 2010

Abstract: In heterogeneous work teams high ability individuals have the possibility of helping less able workers in doing their part of the job. We use experiments to investigate whether, by helping others, some individuals can exercise effective leadership in games meant to capture essential features of some organizational environments. Help is modeled as an activity that lowers others’ costs of effort at the expense of raising one’ own cost. In an initial phase of our experiment helping others is not possible and team performance is very low. The experimental design then explores the effects of varying the financial incentives and of allowing a high ability worker to help the other workers. We find that the possibility of using help round-per-round has only weak effects on the escape from the performance trap. In contrast, if high ability individuals are commited to helping others over an extended period of time, then it has a strong effect. This effect is stronger than when help is exogenously imposed, suggesting that stable relations in work-teams and reciprocity are important for successful organizations.

Keywords: Incentives, Coordination, Experiments, Organizations, Heterogenous work teams

JEL Classification Codes: C92, D23, J31, L23, M52 Acknowledgements: The authors thank the NSF (SES-0214310), the Spanish Ministry of Science and Innovation, the Barcelona GSE research Network and CONSOLIDER-INGENIO 2010 8CSD2006-00016) for financial help.

Authors

Jordi Brandts David. J Cooper Enrique Fatás Dept. of Business Economics U. Autònoma de Barcelona and Institut d’Anàlisi Econòmica (CSIC) Campus UAB 08193 Bellaterra (Barcelona) Spain

Department of Economics Florida State University Tallahassee, FL 32306-2180 USA

Enrique Fatas LINEEX-ERICES Universitat de València Edificio Institutos, Campus Tarongers 46022 Valencia (Spain)

phone 34-93-5806612 fax 34-93-5801452 Jordi.Brandts@uab.es

phone: 850-644-7097 fax: 850-644-4535 djcooper@fsu.edu

phone: (+34) 961 625 161 fax: (+34) 961 625 415 fatas@uv.es

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1. Introduction

This paper studies the role of help between co-workers in firms’ successful escapes from

performance traps. When a company (or other organization) is stuck in a performance trap,

somebody has to take the initiative to start the escape from this situation. Both management and

employees can play a role in this process. Management leadership is an obvious possibility, since

management is directly responsible for the firm’s profitability and has multiple instruments

available to affect a change, such as manipulating the incentive structure or improving its

communication strategy with workers. However, leadership by workers can also play an

important role.

Although help between workers has received little attention from researchers in

economics and management,1 we believe it is a natural instrument for high ability workers to use

in leading the way out of a performance trap. Intuitively, work teams typically contain some

workers that have higher ability than others. If workers are rewarded based on team production,

then high ability workers can have an incentive to take a leadership role by helping less able

workers. The findings of Hamilton, Nickerson, and Owan (2003, 2004) are consistent with this

intuition. They studied the productivity of workers at a garment plant that replaced individual

piece rates with group incentives, a move which involved putting employees into teams. They

found that teams with heterogeneous abilities were more productive. Hamilton et al conjecture

that this was due to the existence of mutual learning, a specific form of help where high ability

types help low ability types understand how work should be done.

In this paper we use laboratory experiments to study help among co-workers. The

provision and impact of help are complex phenomena involving interplay between the effects of

material incentives, beliefs, and non-pecuniary motivations. Laboratory experiments are well

suited for studying settings where these factors interact, as illustrated by Zwick and Chen (1999),

Brandts and Charness (2003), Weber and Camerer (2003) and Harbring and Irlenbusch (2009).

The general virtues of laboratory experimentation in the social sciences are discussed in Falk and

Heckman (2009). The advantages of laboratory experiments for studying help are primarily due

to the control available in experimental settings. We exogenously control whether help is 1 See Brown and Heywood (2009) for a field study on help in settings with individual performance pay. Antonetti and Rufini (2008) for a theoretical analysis of training of low ability types by high ability types, and Bouamod (2006) for a real effort experiment on help in a team setting.

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possible and directly observe how much help is provided. We can therefore cleanly determine

whether help is responsible for observed changes in productivity as opposed to other unobserved

factors. We can also systematically vary how help can be provided, making it possible to pin

down the mechanism by which help leads to improved performance. In addition, in our

experiments we are able to observe in detail the interactive process of giving help and reacting to

help. This greatly enhances our ability to understand the mechanism by which help does (or in

some cases, does not) lead to improved performance.

Our experiments are based on the “corporate turnaround game”,2 an experimental setting

designed to represent a corporate environment in which coordination failure has occurred and

needs to be remedied. This game involves repeated play between a “manager” and four

"employees" of a "firm". We automate the role of the manager while employees are played by

experimental subjects. In each round of the game, the manager first chooses a bonus rate which

determines the fraction of the firm's profits transferred to the employees. After seeing the bonus

rate, the four employees simultaneously choose how much costly effort to expend with firm

output and profits determined by the minimum effort. Critically, the four employees are not

identical. Instead, each group has one high ability type with relatively low effort costs and three

identical low ability types with relatively high effort costs.

As long as the bonus rate for the round is greater than the highest effort cost among the

employees, the game played by the employees is a weak link game (Van Huyck, Battalio and

Beil, 1990). This game has an efficient equilibrium in which all workers choose high effort and

high output and payoffs are realized. Unfortunately, there also exists a Pareto dominated

equilibrium where all workers choose the lowest feasible effort leading to low output and

minimal payoffs for all. Once a firm has fallen into this performance trap, the strong

complementarities between workers’ efforts make a spontaneous escape unlikely, since

improved performance requires a unanimous switch to higher effort. To generate the necessary

coordinated change, some agent must take the initiative of leading the process.

Employees initially face a low bonus rate that makes the minimum possible effort a

dominant strategy for low ability (i.e. high effort cost) types. This serves to trap groups in the 2 The corporate turnaround game was introduced by Brandts and Cooper (2006). For other papers that have used the corporate turnaround game to study overcoming coordination failure, see Hamman, Rick, and Weber (2007) and Brandts and Cooper (2007). In general, there exists an extensive literature on coordination in weak-link games – see Camerer (2003) and Chaudhuri (2009) for surveys. Recent prominent papers include Chaudhuri, Schotter and Sopher (2006), Weber (2006), Blume and Ortmann (2007) and Kogan, Kwasnica and Weber (forthcoming).

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worst outcome possible. The bonus rate is then exogenously increased, turning the game into a

weak link game with multiple Pareto ranked equilibria. The employees now have an opportunity

to escape the performance trap the first phase forces them into. The key issue is whether the

high ability types can use help to assist with this escape.

We define help broadly as a voluntary activity by high ability types that improves the

productivity of low ability types at the cost of decreasing the productivity of high ability types.

Since output in a weak-link game is determined by the individual exerting the least effort, if

providing help leads to increased effort by low ability types, high ability types can gain more by

increasing the productivity of low ability types than it harms them to lower their own

productivity. There are several reasons why help from high ability types might lead to increased

effort by the low ability types. First, there is the direct effect of improving the incentives to

overcome coordination failure for low ability types. Second, a natural forward induction

argument applies. There is no particular reason for high ability types to provide help unless they

believe low ability types will increase their effort. If low ability types understand this point, such

beliefs become a self-fulfilling prophecy. Finally, providing help brings positive reciprocity into

play. Helping is a kind action by high ability types. It is natural to expect that low ability types

will try to reciprocate by choosing a higher effort level. However, this process of improvement

may be jeopardized by the withdrawal of help and negative reciprocity in reaction to that.

As a treatment variable, the possibility of help is introduced in some sessions at the same

time the bonus rate is increased. In keeping with our broad definition of help, we implement help

as a voluntary choice by high ability types that lowers the effort costs of low ability types at the

expense of raising their own effort cost. We systematically vary how help between co-workers

can be provided. In particular, we study the effects of allowing asymmetries and the impact of

forcing high ability types to commit to a level of help. Given that effort is typically asymmetric

in teams which fail to coordinate, it is natural that high ability types might want to provide help

in an asymmetric manner as well. Much of the observed coordination failure is associated with a

failure to commit to some level of help. Intuitively, the issue is that decreasing help has a

negative effect on effort just like increasing help has a positive one. If this negative response is

stronger than the positive one, continually shifting help up and down causes the minimum effort

to ratchet downwards for the group. Forcing high ability types to commit to some level of help

for an extended period of time may improve coordination by limiting the downwards ratcheting.

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Our experimental design contains five treatments, which for expository purposes can be

grouped as Experiments 1 and 2. With the first three treatments - Experiment 1 - we study the

effects of (endogenously chosen) symmetric help and compare it to behavior in the absence of

help and to exogenously imposed help. In the symmetric help treatment the high ability (low

effort cost) worker can, after the bonus increase, help his low ability (high effort cost) co-

workers with different intensities, but must help all three equally. The level of help can be

changed on a round-to-round basis. We find that, as expected, increasing the bonus rate leads to

an improvement in coordination among employees. However, the possibility of providing

symmetric help is quite ineffective in generating further improvements. Resulting minimum

effort levels are no higher than in the control treatment without help and lower than in the

treatment in which help is exogenously imposed. A detailed analysis of how help is used and of

how low ability types react to changes in the level of help suggests two possible origins of this

unexpectedly poor performance. One is the restriction of having to help co-workers identically

when they have behaved differently and the other is a lack of commitment to providing help over

an extended period of time.

Experiment 2 studies these two issues separately. One treatment allows for asymmetric

help without commitment and the other maintains the restriction to symmetric help but forces

high ability types to commit to the chosen level of help for an extended period of time. The

results show that asymmetric help only has a minor impact, but endogenous help with

commitment leads to significantly higher effort levels than symmetric help without commitment.

Moreover, holding the level of help fixed, effort is higher when help is provided endogenously

with commitment then when help is exogenously imposed with the same degree of commitment.

This indicates that the positive effect of help with commitment is not due solely to the direct

effect of changing incentives, but instead a combination of changing beliefs and positive

reciprocity also contributes to the relatively strong performance with commitment. The data

suggests that the change in beliefs plays a more important role than reciprocity.

There are some general points to be taken from our results. Help among co-workers can

be a useful instrument for overcoming coordination failure, but only if it is used in a consistent

fashion. Policies that discourage commitment, such as frequent shifting of work teams, are

likely to destroy the positive effects of help. Because the effect of help is greater if help is

provided endogenously rather than imposed exogenously, policies that encourage voluntary help

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(e.g. giving workers advice about the benefits of help with commitment) are more likely to be

effective than policies that make help mandatory for high ability workers. More work is needed

on how to best generate help and commitment endogenously. More generally, organizational

stability plays an important role in escaping performance traps. Recoordinating on a good

equilibrium doesn’t happen instantly, but instead is a gradual process. Once this process has

been completed, the good outcome is likely to persist even if incentives are changed, but if

incentives change before equilibration has a chance to occur (e.g. help is only provided for a

brief period) then coordination is likely to collapse and play once again becomes stuck in a

performance trap. We hypothesize that the value of stability is a general lesson that applies to

previously studied tools for escaping performance traps, particularly incentive schemes put in

place by management, a conjecture we plan to explore in future work.

Section 2 presents in detail the game that we use in the experiments. Section 3 outlines

the treatments studied in Experiment 1 and section 4 presents the procedures. In section 5 we

present the results of Experiment 1. Sections 6 and 7 present the design and the results of

Experiment 2 and section 8 concludes.

2. The Turnaround Game with Help The “turnaround game” represents a stylized model of the dynamic process by which a

firm tries to escape from a performance trap. This firm consists of a manager and four

employees interacting repeatedly in a fixed group. The firm’s productivity in each round is

determined by employees’ effort choices for the round, with employees’ incentives to exert effort

depending in part on an ex ante profit sharing decision made by the manager. In all of the

experiments reported below the experimenter plays the role of firm manager while experimental

subjects fill the roles of the four employees. Even though the manager’s decisions are

exogenous, it is useful for expositional purposes to treat him as a player in the game. Our

primary interest is in interactions between high and low ability employees, and making the

manager exogenous generates a more controlled environment to study their relations.

The turnaround game embodies three basic design choices. First, the firm’s technology

has a weak-link structure, with productivity (as well as profitability) for each round determined

by the minimum effort chosen by an employee. Second, the firm manager only observes the

minimum effort selected. In other words, the manager observes output but not the individual

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efforts that led to this output. This implies that any incentives the manager gives employees

cannot depend on individual effort. We assume employees can observe all effort levels selected.

Finally, the firm manager rewards employees with bonuses based on the minimum effort

observed. It can change this bonus rate but cannot otherwise influence the employees’ choices.

In what follows we present the main features of the turnaround game in more detail.

An experimental firm in the turnaround game consists of a fixed grouping of four subjects

(employees) who interact for thirty consecutive rounds, broken into three ten-round blocks.

Each block starts with the announcement of a common bonus rate (B) for the ten rounds of the

block that determines how much additional pay each employee receives for each unit increase in

the minimum effort. Intuitively, the bonus transfers part of the firm’s profits to the employees.

All four employees observe B and then simultaneously choose effort levels, where Ei is the effort

level chosen by the ith employee. We restrict an employee's effort to be in ten hour increments: Ei

0 {0,10, 20, 30, 40}. Intuitively, employees spend forty hours per week on the job, and effort

measures the number of these hours that they actually work hard rather than loafing.3

Employees’ payoffs are determined by Equation 1 below. Note that effort is costly, with Ci

denoting the cost of a unit of effort for the ith employee. All payoffs are denominated in

“experimental currency units” (ECUs). These were converted to monetary payoffs at a rate of 1

euro equals 500 ECUs:

Employee i: { }

( )ie i i jj 1,2,3,4π 200 C E B min E

∈

⎛ ⎞= − + ×⎜ ⎟⎝ ⎠

(eq. 1)

In all treatments the average cost of effort equals 7, ( )( )11 2 3 44i.e. C + C + C + C = 7 .

Unless otherwise noted, Employee 1 will be a high ability type with an initial effort cost c1 =1

while the other three employees are low ability types with initial effort costs c2 = c3= c4 =9. In

treatments with help, as described in Section 3, the final effort costs will differ from these as a

function of how much help is provided.

Consider the game played in a single round when help is not possible. Table 1 shows the

payoffs for each type if B=8. For a high ability type (i.e. Ci = 1) the best response depends on the

minimum effort of the other workers, but it is a dominant strategy for low ability types (i.e. Ci =

3 In the experiments, terms that we judged to have strong connotations such as “effort” and “loafing” were not used. Employees were told that they spent 40 hours per week on the job, and that these hours could either be allocated to Task A or Task B. Task A plays the role of effort and Task B plays the role of loafing.

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9) to choose zero effort. It follows that for B=8 the game is not a weakest-link game. In the

unique Nash equilibrium all employees exert zero effort. We use the game with B=8 to get play

stuck in a performance trap. This cannot be classified as coordination failure, since there doesn’t

exist an equilibrium with positive effort exerted, but instead sets a strong precedent of low effort

for games where coordination at high effort is possible.

Table 1

Employee i’s Payoff Tables for B=8

Ci = 1 Ci = 9

Minimum Effort by Other Employees

Minimum Effort by Other Employees

0 10 20 30 40 0 10 20 30 40

Effo

rt by

Em

ploy

ee i 0 200 200 200 200 200

Effo

rt by

Em

ploy

ee i 0 200 200 200 200 200

10 190 270 270 270 270 10 110 190 190 190 190 20 180 260 340 340 340 20 20 100 180 180 180 30 170 250 330 410 410 30 -70 10 90 170 170 40 160 240 320 400 480 40 -160 -80 0 80 160

Now imagine that, after a long stretch of bad performance, the manager tries to improve

performance by permanently changing the bonus rate from B=8 to B=14. Table 2 shows the new

payoff tables for the two types of employees. The game is now a weakest-link game.

Coordination by all four employees on any of the five available effort levels is a Nash equilibria.

The problem faced by the employees is a strong precedent of choosing the lowest possible effort

level. Consider the incentives faced by the employees if they try to jump from the lowest

minimum effort level to the highest (0 to 40). For simplicity assume that all employees will

either choose 0 or 40 for their effort level. For a high ability type, the incentives are fairly good.

Increasing effort to 40 incurs an effort cost of 40 ECUs which is sunk. The potential gain is 520

ECUs. For this increase to have positive expected value, the probability of the three low ability

types all increasing to effort level 40 must only be greater than 1/14. The odds are much rougher

for the low ability types. They must sink an effort cost of 360 ECUs and can only potentially

gain 200 ECUs. For this to have a positive expected payoff, the probability of the high ability

type and both low ability types increasing their effort to 40 must be greater than 9/14. Low

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ability types must be far more optimistic than high ability types to be willing to take the risk of

increasing their effort levels.

Table 2

Employee i’s Payoff Tables for B=14

Ci = 1 Ci = 9

Minimum Effort by Other Employees

Minimum Effort by Other Employees

0 10 20 30 40 0 10 20 30 40

Effo

rt by

Em

ploy

ee i 0 200 200 200 200 200

Effo

rt by

Em

ploy

ee i 0 200 200 200 200 200

10 190 330 330 330 330 10 110 250 250 250 250 20 180 320 460 460 460 20 20 160 300 300 300 30 170 310 450 590 590 30 -70 70 210 350 350 40 160 300 440 580 720 40 -160 -20 120 260 400

The apparent advantage of high ability types only matters if they can get low ability types

to increase their effort. The flip side of high ability types having good incentives to try to

coordinate is that they also have strong incentives to try to influence the turnaround process after

seeing the new bonus rate. One way they might do this is by helping low ability types. We have

defined help broadly as a voluntary activity by high ability types that improves the productivity

of low ability types at the cost of decreasing the productivity of high ability types. For our

experiment we operationalize help as a voluntary choice that decreases the effort cost of a low

ability type for a round at the expense of increasing the high ability type’s effort cost for the

same round. We assume the cost of help is 1 to 1 – lowering one of the low ability type’s effort

cost by one unit raises the high ability type’s effort cost by one unit. To simplify the experiment,

low ability types are not allowed to help others. Given their already high costs, we think it is

unlikely they would provide help even if allowed to do so. Only allowing one player to provide

help eliminates additional coordination problems such as who is supposed to be providing

leadership and how to coordinate help if more than one individual provides it.

The kind of help that we study has two notable features: the effect of help is indirect

(high ability types don’t do low ability types’ work, they make it less costly for them to do their

own work) and temporary. Implementing help with these features has the advantage of being

simple and keeping the basic features of the game close to those of a standard weak-link game.

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Eliminating dominated strategies,4 any subgame that occurs after choosing a level of help is a

weak-link game. The strategic issues facing workers in the standard turnaround game are still

present in the turnaround game with help. Once we understand the effects of this relatively

simple version of help, a natural follow-up is to study how these results extend to experiments

modeling other varieties of help.5

There are several reasons to believe, ex ante, that the simple type of help included in our

game can be an effective tool in promoting a successful turnaround. The obvious one is that help

improves the incentives for high ability employees to switch to higher effort level. This effect is

surprisingly small. Suppose Employee 1 offers sufficient help to lower the cost of effort for all

low ability type to 7, thereby raising his own effort cost to 7 as well. Once again consider the

incentives to move from 0 to 40. This requires a (sunk) effort cost of 280 ECUs and potentially

gains 280 ECUs. To have a positive expected payoff, the probability of the three other players

increasing their effort to 40 must be greater than 1/2. This is not much different from the 9/14

chance needed for low ability types without help. Given that the incentives have gotten far

worse for the high ability type, it isn’t clear that this modest change in incentives for low ability

types will make much difference.

Given that changing incentives don’t seem likely to have much effect on the likelihood of

a successful turnaround, why do we believe providing help will be useful? One possibility is that

Employee 1’s decision to help reinforces the impact of the bonus rate increase as a coordination

device. In other words, providing help makes low ability types believe it is more likely that

others will increase their effort and hence more likely to increase their own effort. This is in the

spirit of a forward induction argument: high ability types cannot gain from providing an

increased amount of help unless the group’s minimum effort increases. Thus an increase in help

4 Offering a level of help that increases the high ability type’s cost of effort above the bonus rate is a weakly dominated strategy for a single play of the game. 5 Both direct help and permanent help can also be implemented in laboratory experiments at the cost of greatly increasing the complexity of the problem facing subjects. To operationalize direct help, suppose the four workers of a firm can either keep their tokens or put them into one of four bins, with one bin assigned to each worker. Total output is determined by the bin that receives the smallest number of tokens. Workers are paid a fixed amount for each token they keep as well as a bonus rate multiplied by the amount of output. Differing ability is induced by giving the tokens different values for different workers. If workers can only put tokens into their own bin, this is exactly equivalent to a weak link game. Help is added by allowing workers to put tokens into other worker’s bins. This new game fundamentally changes the nature of the problem facing workers since it is no longer a weak link game. For example, notice that a worker can now unilaterally increase the output. For permanent help, the effect of a high ability type providing help in the current can be made a permanent reduction in the effort cost of low ability types. This change in the game faces high ability types with a complex dynamic optimization problem.

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signals a belief that minimum effort will increase.6 In weak-link games, believing that others

will choose a higher effort level tends to be a self-fulfilling prophesy. If knowing that the high

ability type believes minimum effort will increase makes low ability types also believe that

minimum effort will increase, then it is likely that minimum effort will indeed increase as

expected!

The effect of providing help on beliefs is subtly different from the effect of cheap talk.

On the one hand, providing help is less explicit than a statement that all employees should

choose a higher effort level, but on the other hand providing help may be more credible than

cheap talk since it is costly to the low ability type if minimum effort does not increase.

Finally, elements of reciprocity – in the sense of rewarding kind actions - may come into

play. When helping a low ability worker, the high ability worker gives up some payoffs to the

low ability type holding the effort levels fixed. The employee being helped may feel grateful and

exert an effort level that goes beyond the one that corresponds to the more favorable incentives

and to the changes in beliefs about others’ actions. If this gift exchange is sufficiently strong, it

provides high ability types with a positive incentive to increase help. The flip side of this is that

effort may be reduced following a reduction of help as an expression of negative reciprocity.

3. Experiment 1: Symmetric Help Without Commitment vs. Exogenous Help

For expository purposes, we divide the five treatments in our experiment into two

experiments. Experiment 1 studies the effects of allowing for the simplest variety of help and

compares it to two natural baseline treatments. In all three treatments, subjects played thirty

rounds in fixed groups (“firms”) of four subjects (“employees”). The bonus was fixed at B = 8

for the first ten-round block, to get subjects locked into the performance trap from which they

would subsequently try to escape. In the second and third ten-round blocks the bonus was set to

6 Similar forward induction arguments about coordination in median games and the effect of markets or fees for entry are made by Van Huyck, Battalio and Beil (1990) and Cachon and Camerer (1996) respectively. As is the case in those papers (see Crawford and Broseta, 1998), formal forward induction arguments do not give a tight prediction in our game. The high ability type makes a guaranteed payoff by choosing to provide no help and choosing effort level 0. He can only expect to make a strictly greater payoff when providing help if he expects the minimum effort to be greater than zero. However, if the high ability type plans to choose effort level 0, providing help has no impact on his payoffs. Thus, it cannot be argued that a high ability type providing help must be believed to be choosing a strictly positive effort level. Even if the low ability types believe that the high ability type will choose positive effort, the low ability types might still choose zero if they do not believe the other low ability types will choose positive effort. Thus, while we believe the forward induction argument is quite relevant in our game with help, we need to be clear that this is an intuitive rather than a formal argument.

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B = 14, converting the game into a weak-link game. The bonus rate was announced at the

beginning of each of the three ten-round blocks and was fixed during that time frame. While

playing in a block with a particular bonus rate, subjects did not know what the bonus rate would

be in subsequent ten-round blocks.

Table 3 List of Treatments of Experiment 1

TREATMENT NAME NO HELP ENDOGENOUS HELP

EXOGENOUS HELP

Player 1 Cost Block 1 1 1 1

Player 1 Cost Blocks 2 and 3 1

1 + 3H { }H 1,2,3,4∈ 7

Players 2, 3 & 4 Cost Block 1 9 9 9

Players 2, 3 & 4 Cost Blocks 2 and 3 9

9 – H { }H 1,2,3,4∈ 7

Number of Firms (Number of Sessions)

20 (2 Sessions)

39 (5 Sessions)

20 (2 Sessions)

Table 3 summarizes the three treatments in Experiment 1. The treatments vary with

respect to how the effort costs are determined in the different blocks. During the first ten rounds

effort costs were exogenously fixed in all treatments at C1 = 1, C2 = C3 = C4 = 9. In the No Help

treatment, help was not possible and effort costs remained exogenously fixed at the initial levels

throughout rounds 11-30.

In rounds 11 – 30 of the Endogenous Help treatment Employee 1 has the option of

providing each low ability employee with 0, 1, 2, 3 or 4 units of help ( { }H 1,2,3,4∈ ).

Restricting the high ability type to offering all three low ability types the same level of help

simplifies their task since they only need to make one choice when assigning help rather than

three. The high ability type chose a help level in each round after seeing feedback about effort

choices in the previous round but before any effort choices were made for the current round. In

other words, the high ability types pre-commit to a level of help for the current round (but not for

future rounds). This contrasts with the bonus rate which is fixed for a ten round block.

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For the first three levels of help, which constitute 94% of all observations, offering help

corresponds to:

a. (H = 0) Leaving the effort cost distribution at: 1, 9, 9, 9.

b. (H = 1) Reducing each of the three co-worker’s effort cost by 1 and increasing own

effort cost by 3, leading to a cost distribution of 4, 8, 8, 8.

c. (H = 2) Reducing each of the three co-worker’s effort cost by 2 and increasing own

effort cost by 6, leading to a distribution of 7, 7, 7, 7.

Help levels of 3 and 4 modify the distribution of effort cost in an analogous way. At

these help levels Employee 1 assists the others so much that his costs of effort are higher than

those of low ability types. It is therefore not surprising that use of help levels 3 and 4 is rare.

Looking at the final line of Table 3, note that we ran twice as many groups for the

Endogenous Help treatment as the two baseline treatments. This was done to give us a better

opportunity to study how low ability types responding to changes in the amount of help provided

by high ability types.

In the “Exogenous Help” treatment, the distribution of effort costs is exogenously

switched for Blocks 2 and 3 to the symmetric distribution with a common cost of 7. We include

this treatment to disentangle the direct effects of help on employees’ effort levels (i.e. effects due

to changing the incentives to increase effort) from indirect effects due to forward induction and

reciprocity. The switch in effort costs for Blocks 2 and 3 is equivalent to exogenously imposing

H = 2, but because the high ability type has no control over this change it neither signals

anything about his beliefs nor can it be interpreted as a kindness by the high ability type. Effort

costs in the Exogenous Help treatment were held constant held for ten-round blocks, a fact which

was common knowledge among employees. As a consequence, in this treatment there is

effectively a commitment to H = 2 for the block.

For rounds 1 – 10 in all three treatments, we expected average minimum effort to be close

to zero since this is the unique equilibrium (and a strictly dominant strategy for low ability

types). The intent is to have all groups facing a history of low effort when the bonus increase

and help (possibly) becomes available. For all treatments we anticipated an increase in

minimum effort for rounds 11 – 30 since the bonus rate had increased – Brandts and Cooper

(2006a) find that bonus rate increases in the turnaround game reliable lead to high minimum

effort on average. The important question is whether symmetric help, either offered

13

endogenously or imposed exogenously, leads to an even greater increase in minimum effort

levels. Based on our discussion of possible effects of help, we formulate two initial hypotheses.

H1 amounts to hypothesizing that help has a direct effect through its impact on incentives to

coordinate while H2 is based on the hypothesis that endogenously provided help will have a

greater impact due to a combination of forward induction and positive reciprocity.

H1: In the long run, average minimum effort will be higher in the Endogenous Help and

Exogenous Help treatments than in the No Help treatment.

H2: In the long run, average minimum effort will be higher in the Endogenous Help treatment

than in the Exogenous Help and No Help treatments.

4. Procedures Subjects were recruited from the undergraduate population of the University of Valencia

using an electronic recruitment system. All sessions were run at the LINEEX computer lab of the

University of Valencia. Subjects were only allowed to participate in a single session and had no

previous experience in similar experiments.

The experimental procedures were fairly standard. At the beginning of each session

subjects were randomly seated. Printed instructions were distributed and read aloud by the

experimenter. The instructions stress that there are two types of employees with differing payoff

tables. Before beginning play, all subjects were asked to complete a short quiz about the payoffs

and the rules of the experiment. The full text for the instructions is given in Appendix A.

The instructions used a corporate context to make them easier to understand for

participants. For example, the four players are explicitly referred to as "employees" and are told

that they are working for a "firm." We avoided the use of terms with strong connotations. For

example, instead of asking subjects to choose a level of "effort" they are asked to allocate time

between "Activity A" and "Activity B," with Activity A playing the role of effort. While we

doubt that the use of a corporate context causes any demand induced effects, it is always possible

that the use of meaningful context per se has some impact on subjects' choices. Presumably any

such effect is constant across treatments.

Subjects play the game in a fixed cohort of four employees. The instructions stressed that

the groups were fixed for the duration of the experiment. The field settings that motivated these

14

experiments involve repeated interactions among the same agents and repeated game effects and

strategic teaching are presumably quite natural in these settings.7

At the beginning of each ten-round block employees were informed of the bonus rate for

that block. Employees were not told what bonus rates would be in subsequent blocks. In each

round of the No Help and Exogenous Help treatments the four employees of a firm

simultaneously chose their effort levels for the round. While choosing, the employees were

shown a payoff table, similar to those displayed in Tables 1 and 2, showing their payoff as a

function of their own effort level and the minimum effort level chosen by the other employees.

This payoff table was automatically adjusted to reflect the current bonus rate. Subjects also had

a printed copy of the payoff table for employees with different effort costs.

At the end of each round, all employees saw a feedback screen showing them their effort

level, the minimum effort for their firm, their payoff for the round, and their running total payoff

for the experiment. Separate windows on the feedback screen showed them a summary of results

from earlier rounds and the individual effort levels selected for all four employees in their firm.

These effort levels were sorted from highest to lowest and did not include any identifying

information about which employee was responsible for which effort level.

Subjects in the Endogenous Help treatment received additional printed instruction before

the start of the second block explaining how help worked. These stressed the relationship

between the costs of the two types – high ability types lower the costs of others at the expense of

raising their own costs – and also provided all players with all possible payoff tables that could

occur for either type of player with some feasible level of help. Subjects were not told about the

possibility of help prior to this point in time, so all three treatments are parallel until the

beginning of the second block. Subjects in the No Help and Exogenous Help treatments did not

receive new instructions prior to the second block.

The timing of rounds 11 – 30 in the Endogenous Help treatment differs from those in the

other two treatments. After seeing the feedback from the previous round, the high ability type

selected a level of help to provide. All employees saw the level of help selected as well as the

resulting costs for the two types. All four employees then simultaneously made effort decisions.

The payoff table they saw while making this decision was adjusted to reflect the amount of help

7 There exist several papers comparing coordination with fixed and random matching. These uniformally find that coordination is more difficult with random matching (Van Huyck et al, 1990; Clark and Sefton, 2001; Chaudhuri and Paichayontvijit, 2009).

15

provided by the high ability type. Printed payoff tables were available to see the payoffs of the

other type.

At the end of the session, each subject was paid in cash for all rounds played plus a show-

up fee. Payoff was done on an individual and private basis. The average total payoff was

€21.60, including a five euro show-up fee. These earnings were sufficiently large to generate a

good supply of subjects.

5. Results for Experiment 1

Before outlining the results, it is useful to reiterate our terminology. “Employee” refers

to an individual subject in the experiment while “firm” refers to a fixed grouping of four

employees. Thus, “employee-level” data consist of four separate effort levels per round per firm,

one choice per employee. “Firm-level” data consists of a single observation per round per firm,

the minimum effort chosen by the four employees of the firm. Whenever we refer to “effort” or

“average effort,” we are referring to employee-level data. If we refer to “minimum effort” or

“average minimum effort,” we mean firm-level data.

Figure 1 shows average minimum effort in the Endogenous Help treatment together with

the data from the two control treatments, the No Help and Exogenous Help treatments. In round

10, the last round prior to the bonus rate increase, all firms had a minimum effort of zero. This is

expected given that a common effort level of zero is the only equilibrium of the stage game with

B=8, but remains important to note since a history of low effort is a precondition for our

environment to be of interest.

Focusing on the turnaround process in rounds 11-30, Figure 1 shows that minimum effort

is roughly the same in the Endogenous Help treatment as in the No Help sessions and somewhat

higher in the Exogenous Help treatment than in either of the other two treatments. Comparing

average effort at the employee level yields a similar picture. The exogenous bonus increase

helps firms escape the performance trap and exogenously imposed help somewhat increases this

improvement, but, surprisingly, the possibility of high ability workers endogenously helping low

ability workers does not add to the improvement.

Regression analysis contained in Appendix B provides a formal statistical backing for the

preceding conclusions. These ordered probit regressions correct for clustering at the group level

and include controls for behavior in the initial phase, Rounds 1 – 10. The only significant

difference we find between treatments in Experiment 1 is between the Endogenous and

16

Exogenous Help treatments in Rounds 21 – 30, and this is weak. The regression results reinforce

our casual impressions from the raw data – endogenous help does nothing to improve firm

productivity (as measured by minimum effort) and even the positive effect of exogenous help is

modest. The data shows no support for either H1 or H2.

Figures 2 and 3 show payoffs for high and low ability types respectively, broken down by

treatment. Looking at Figure 2, average payoffs for high ability types are roughly the same for

sessions with either Exogenous or Endogenous Help. Both are substantially lower than average

payoffs with No Help. Running OLS regressions with equivalent specifications to those

described in Appendix B with high ability type profits as the dependent variable, the difference

in high ability type payoffs between the No Help and the Endogenous (Exogenous) Help

treatment is statistically significant at the 5% (1%) level in Rounds 11 – 20 and at the 10% (10%)

level in Rounds 21 – 30.

Figure 3 shows the flip side of the coin. Average payoffs for low ability types are roughly

the same for the Endogenous Help and No Help treatments. Both are substantially lower than

average payoffs for the Exogenous Help treatment. Regression analysis finds that the differences

in low ability type payoffs between the Exogenous Help treatment and the Endogenous Help and

No Help treatments are statistically significant in Rounds 11 – 20 at the 5% level and at the 1%

level in Rounds 21 – 30.

To summarize, the Endogenous Help Treatment is the worst case scenario for payoffs.

It isn’t so surprising that Endogenous Help makes high ability types worse off – after all, help is

costly. The surprise is that Endogenous Help doesn’t make low ability types better off even

though they benefit from receiving help. In other words, Endogenous Help doesn’t even

generate a positive transfer from high to low ability types.

Conclusion 1: Endogenous Help does not improve firm productivity, as measured by minimum

effort. Endogenous Help harms high ability types without benefiting low ability types. The data

does not support either H1 or H2.

The turnaround game with endogenous help is a complex dynamic game. Help can be

changed at any point as high ability types react to the effort choices of low ability types (and vice

versa). To better understand why Endogenous Help does so little to improve firm productivity,

we need to carefully examine the interaction between help and effort.

17

Before doing so, we digress to examine two simple potential explanations for the poor

performance with endogenous help. One possibility is that high ability types fail to use help.

However, help is used extensively throughout the Endogenous Help treatment. Positive help is

used in 70% of observations, 37 of 39 high ability types (95%) provide a positive amount of help

at least once, and 36 of 39 high ability types (92%) provide positive amounts of help in at least

25% of the periods. On average, 1.21 units of help per low ability type are provided, a level

which changes little over time. Poor performance in the Endogenous Help treatment cannot be

attributed to an unwillingness to provide help.

A closely related possibility is that high ability types provide insufficient help. Less help

is provided, on average, in the Endogenous Help treatment than in the Exogenous Help

treatment. Exogenously provided help has a modest positive effect on minimum effect,

presumably due to changing incentives, so perhaps the same positive incentive effect would

emerge in the Endogenous Help treatment if only high ability types were more helpful. The data

is not consistent with this explanation. First, if the only issue was the amount of help provided,

we’d expect the average minimum effort in the Endogenous Help treatment to fall between the

other two treatments rather than being the lowest. Also, if the question was strictly one of

incentives, we’d expect the average minimum effort to be an increasing function of help. This is

not true. With no help, the average minimum effort in Rounds 11 – 30 of the Endogenous Help

treatment is 18.9 (235 obs.). When one unit of help is provided, the average minimum effort

falls to 12.7 (224 obs.). This rises to 25.3 (273 obs.) with two units of help but falls again to 4.0

(48 obs.) when three or more units of help are provided. This isn’t to say that incentives don’t

matter, but clearly something else must be going on as well in the Endogenous Help treatment.

To locate this “something else” we examine the dynamic interaction of help and effort.

Figure 4 shows the effect of high ability types changing their help levels on the average

minimum effort levels of the low ability types in a firm for Rounds 12 – 30.8 Round 11 is not

included since the effect of help is confounded with the bonus rate increase. Changes in the

amount of help clearly affect the minimum effort of the three low ability types. When the lagged

minimum effort of the low ability types is 0, improvement is the only possibility. Such

improvement mainly occurs when help is increased. If the lagged minimum effort for the three

low ability types is 40, only decreases are possible. This is far more likely after a decrease in the 8 An observation here is the minimum effort by the three low ability types in a firm for a single round.

18

level of help. The most interesting case is when the lagged minimum effort level for low ability

types is 10, 20, or 30. Given that most groups which successfully coordinate do so gradually,

these cases are critical ones in determining the firm’s success. Increasing help or holding it

constant only has a moderate effect on minimum effort levels for low ability types, but

decreasing help has a strong negative on their minimum effort levels. It appears that the negative

effect of a decrease to help is greater than the positive effect of an increase.

Table 4: The Effect of Changes in Help on Effort by Low Ability Types

Model 1 Model 2

Dependent Variable

Firm-Level Data Min. Effort, Low Ability Types

Employee-Level Data Effort, Low Ability Types

Current Level of Help .044 (.062)

.045 (.066)

Increase in Help * (Change in Help > 0)

.218*** (.082)

.124** (.060)

Decrease in Help * (Change in Help < 0)

-.604*** (.137)

-.377*** (.059)

Log Likelihood -674.65 -2416.30

Number of Observations 780 2340

Notes: Standard errors are corrected for clustering at the firm level. Three (***), two (**), and one (*) stars indicate statistical significance at the 1%, 5%, and 10% respectively.

Figure 4 provides suggestive evidence that the response to changes in help are

asymmetric, but only roughly controls for the lagged minimum effort, provides no control for the

time effects that are so obvious in Figure 1, and does not disentangle effects of changing help

from the effect of the current level of help. Because the response of low ability types to

changing help is critical for understanding why allowing symmetric help does not lead to

improved minimum effort, it is important to address these issues. Table 4 therefore shows the

results of ordered probit regressions meant to capture the relation between changes in help and

effort levels more precisely. The dataset is all observations where help was available (Rounds 11

– 30) for the Endogenous Help treatment. Model 1 uses firm-level data with the dependent

variable being the minimum effort chosen by the firm’s three low ability types in the current

round. Model 2 uses employee-level data from low ability types only. The dependent variable is

the chosen effort level for the current round. Given that these dependent variables are ordered

19

categories, use of an ordered probit specification is natural. As should be clear from Figures 1

and 4, the current period and the lagged (minimum) effort both play an important role in

determining how the (minimum) effort changes beyond any change in the level of help provided.

To control for these effects, both regressions include dummies for the current round9 as well as

dummies for each possible value of the lagged dependent variable (lagged minimum effort by

low ability types in Model 1, lagged effort in Model 2).10 Parameter estimates for these dummies

and the cutoffs are not reported in Table 4 since they are not of direct interest. Copies of the full

regression output are available from the authors upon request. The primary independent

variables are the current level of help, the increase in help from the previous period interacted

with a dummy for a positive change in help, and the decrease in help from the previous

interacted with a dummy for a negative change in help.11 Standard errors are corrected for

clustering at the firm level.

Looking at Model 1, the two coefficients for changes in the level of help are both strongly

significant, while the one for the current level of help is not. Changes in the minimum effort of

low ability types are driven more by changes in the level of help than the amount of help

provided currently. The negative coefficient for negative help changes is almost three times as

large – in absolute terms - as the positive one for positive help changes. The difference between

the absolute values of these two parameters is statistically significant at the 1% level.

Controlling for the current round and the recent history of play, the effect of a decrease in help is

much greater than the effect of an increase. The main results for Model 2 are much the same: the

level of help does not have a significant effect and the negative effect of decreasing help is

roughly three times as large as the positive effect of increasing help with the difference being

statistically significant at the 1% level. One possible explanation for the asymmetric response of

minimum effort to changes in help is strictly mechanical – three individuals need to respond

positively to increased help to raise the minimum effort for low ability types, but only one needs

to to respond negatively to decreased help to lower the minimum effort. The results of Model 2

indicate that the disproportionate response to decreases is not caused by the minimum function

9 Inclusion of round dummies also controls for the effect of the bonus rate increase prior to Round 11. 10 To avoid colinearity, the dummies for Round 11 and lagged (minimum) effort = 0 are dropped. 11 To be clear, decreases are being measured as positive numbers. For example, if a high ability type decreases help from 2 to 0, the variable “Decrease in Help * (Change in Help < 0)” equal 2, not -2.

20

emphasizing decreases. We defer further discussion of explanations for the asymmetric response

to help until after the results for Experiment 2 have been presented since the data from these

additional treatments is necessary for addressing this issue.

Conclusion 2: The negative effect of decreasing help on effort by low ability types is roughly

three times greater than the positive effect of increasing help.

Figure 5 reveals why it is so important that the response to decreasing help is greater than

the response to an increase. Figure 5 shows the relation between the number of changes in help

and both the minimum effort levels of low ability types and the payoffs of high ability types.

Firms from the Endogenous Help treatment are broken into categories by how many times the

level of help was changed in Rounds 11 – 30. It is striking how often high ability types changed

how much help they were providing. The median number of changes to help over 20 rounds was

6, or roughly one change every three rounds. About a quarter of the high ability types, 10 of 39,

changed the level of help in at least half of the rounds. Given that there are only three help levels

that get frequent use, this means that many high ability types were oscillating back and forth

between high and low help levels. If the effect of help on effort by low ability types was solely

due to changing incentives, this instability might matter little. However, as shown above, the

effect of a decrease is much greater than the effect of an increase. Therefore, we would expect

the constant shifting of help to cause a racheting down in the minimum effort of low ability types

and, by extension, the payoffs of this ability types. Figure 5 indeed shows that frequent changes

in help are associated with lower levels of minimum effort by low ability types and low payoff

levels for high ability types.

The preceding suggests that a lack of commitment is at the root of poor performance in

the Endogenous Help treatment. Exacerbating this problem is when help is changed. Figure 6

displays the likelihood for Rounds 12 - 30 of help being decreased, kept the same, or increased

as a function of the lagged minimum effort of low ability types. Once again, Round 11 is not

included since there is a confound with the bonus rate increase. High ability types are more

likely to change the level of help they provide when the lagged minimum effort of the low ability

types is low. The direction of the change also depends on the lagged minimum effort of the low

ability types, with increases more likely when lagged minimum effort is low and decreases more

likely when lagged minimum effort is high (subject to a change occurring). This tendency to cut

help when things are going well is likely due to attempts at profit taking by high ability types –

21

they have gotten the firm (somewhat) out of its performance trap and seek to reap their reward

by reducing the help they provide. This seems like a sensible approach, but is actually a bad

strategy given the strong negative response by low ability types to decreased help. Just as things

are going well, high ability types tend to throw a wrench in the works by decreasing help.

To summarize, the data suggests that a lack of commitment by high ability types,

especially a tendency to slash help when things are going well, leads to poor performance in the

Endogenous Help treatment. This explanation is not watertight since we have not established a

causal relationship. Inconsistency is associated with poor performance, but the opposite is true

as well since high ability types are more likely to change help when the low ability types have

been choosing low effort levels. The Commitment treatment in Experiment 2 is designed to

establish a causal relationship between commitment and performance.

Another feature of the Endogenous Help treatment which may reduce the impact of help

is that all low ability types must be helped with the same intensity. We imposed symmetric help

to simplify the problem facing high ability types, but it may deny them a valuable tool given that

the behavior of low ability types is frequently asymmetric and poor performance is associated

with asymmetric effort by low ability types.

Table 5: Likelihood that exactly one low ability type determines the minimum effort

MINIMUM EFFORT OF LOW ABILITY WORKERS 0, 10, OR 20 30 OR 40

Rounds 11-15 (Number of observations)

.591 (132)

.190 (63)

Rounds 16-20 (Number of observations)

.328 (128)

.104 (67)

Rounds 21-25 (Number of observations)

.429 (119)

.053 (76)

Rounds 26-30 (Number of observations)

.122 (98)

.031 (97)

Table 5 uses data from the Endogenous Help treatment to illustrate this problem. We

focus on a specific type of asymmetry where one of the low ability types chooses a lower effort

than the other two. In other words, these are cases when there truly is a weak link. Not only is

this type of asymmetry common, it is also strongly associated with poor performance. It is

unsurprising that the minimum is usually not uniquely determined for the higher minimum

efforts (30 and 40). Most of these observations are cases where all three low ability types are

choosing 40. The interesting part is that in a high percentage of observations where the

22

minimum effort of low abilty types is relative low (0, 10, or 20), including more than half the

cases in the critical early rounds, a single individual choosing low effort is the culprit. This

highlights the potential importance of being able to use help in asymmetric ways.

If one individual is holding back the group, it seems quite natural that the high ability

type might want to treat this person differently. Perhaps they are given more help than others to

encourage them to risk a higher effort level. Maybe they are punished with a lower level of help

than others. Given that behavior is asymmetric, why should help be symmetric? If asymmetric

assignments of help can be used to nudge laggards to higher effort levels, allowing help might

lead to better performance rather than worse performance. The Asymmetric Help treatment in

Experiment 2 allows for this possibility.

6. Experiment 2: Commitment and Asymmetric Help Experiment 2 studies the impact of forcing commitment or allowing asymmetric help on

the ability of groups to escape performance traps. Table 6 presents the detail of the two new

treatments. Block 1 (Rounds 1 – 10) is unchanged from Experiment 1.

In Blocks 2 and 3 (Rounds 11 – 30), the Asymmetric Help treatment differs from the

Endogenous Help along two dimensions. As in the Endogenous Help treatment, the high ability

type (Employee 1) can help the low ability types (Employees 2 – 4) by a choosing level of help

on a round to round basis. Unlike the Endogenous Help treatment, differing levels of help can be

selected for the three different low ability types ( { }H 0, 1, 2, 3, 4i ∈ ). The transformation rate

is 1 to 1, as in the Endogenous Help treatment. With this modification Employee 1 can, for

example, decide to reduce Employee 2’s effort cost by four units without changing the effort

costs of the other two workers (perhaps in the hope of making Employee 2 a co-leader in the

process of escaping a performance trap). The resulting cost distribution would be H1 = 5, H2 = 5,

H3 = 9, and H4 = 9.

The differing nature of help in the Endogenous and Asymmetric Help treatments led us to

implement different information feedback rules. In the Endogenous Help treatment, employees

were informed about all employees’ effort levels after each round (sorted from highest to

lowest), but without attaching any kind of individual identification to the effort levels. In

contrast, in the Asymmetric Help treatment each employee had an identification number that was

reported along with their effort as part of the feedback. This made it possible for the high ability

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type to track individual effort levels over time and use this information for assigning differing

levels of help.12

Table 6: List of Treatments for Experiment 2

TREATMENT NAME ASYMMETRIC HELP COMMITMENT

Player 1 Cost Block 1 1 1

Player 1 Cost Block 2 and Block3 { }

2 3 41 + H + H + HH 0,1,2,3,4i ∈

1 + 3H (H fixed for block)

{ }H 1, 2,3, 4∈

Players 2, 3 & 4 Cost Block 1 9 9

Player 2, 3 & 4 Cost Block 2 and Block3

(9 – Hi) i ∈ {2, 3, 4}.

9 – H (H fixed for block)

Number of Firms (Number of Sessions)

21 (2 sessions)

20 (2 sessions)

In the Commitment treatment, the high ability type (Player 1) chooses how much

help to provide only in Rounds 11 and 21. In these two rounds Player 1 sets the level of help in

exactly the same fashion as in the Endogenous Help treatment. Specifically he chooses

{ }H 0, 1, 2, 3, 4∈ and the effort cost of all three low ability types is lowered by this amount.

As in the Endogenous Help treatment, the same amount of help must be provided to all three low

ability types. Player 1’s effort cost increases by 3H. Unlike the Endogenous Help treatment,

where help is chosen for each round, in the Commitment treatment the high ability type must

stick to his decision for the entire ten-round block. In other words, we force the high ability type

to commit to a help level. This prevents the frequent changes to the level of help observed in the

Endogenous Help treatment. Effort levels are still chosen round-by-round as in the other

treatments.

12 Normally in putting together an experimental design we’d be careful to only change one thing at a time. However, it seemed unlikely that asymmetric help would have any effect in the absence of an ability to track individual effort levels, a conjecture that was supported by a small scale trial of ten groups where asymmetric help was allowed without the ability to track individual effort levels. There is no particular reason to believe that tracking individual effort levels by itself will lead to an increase in minimum effort. If the Asymmetric Help treatment had a more dramatic effect on minimum efforts we would have confirmed this conjecture, but given the modest effect we find there was little reason to do so.

24

For both of the new treatments our initial hypothesis, summarized in H3, was that

minimum effort levels should be higher than in either the No Help treatment or the Endogenous

Help treatment.

H3: In the long run, average minimum effort for both the Asymmetric Help and Commitment

treatments will be higher than either the No Help or Endogenous Help treatments.

Figure 7 shows the effect on average minimum effort for all five treatments, modifying

Figure 1 by adding data from the two new treatments (Asymmetric Help and Commitment).

Compared with either the No Help or Symmetric Help treatments, Asymmetric Help has a

modest positive effect which largely disappears by the end of the experiment. The Commitment

treatment yields obviously higher minimum efforts than either the No Help or Symmetric Help

treatments, a difference that grows between the first and second block. Minimum efforts in the

Commitment treatment are moderately higher than in the Exogenous Help treatment for both

blocks. Looking at effort rather than minimum effort leads to similar conclusions – the

Commitment treatment leads to a substantial and persistent increase in effort levels over the No

Help and Symmetric Help treatments.

Figures 8 and 9 show payoffs for high and low ability types, respectively, for all five

treatments from Experiments 1 and 2. Asymmetric Help does slightly better than Endogenous

Help for both types. More dramatically, the Commitment treatment always does (roughly) as

well as the best of the other treatments for the final block. Unlike the Endogenous Help

treatment, which is the worst of all worlds, the Commitment treatment is the best of all worlds!

The regression analysis describe in Appendix B reinforces our impressions of the data.

Compared with either the No Help or Endogenous Help treatments, the Asymmetric Help

treatment does not have a statistically significant effect on minimum effort or effort. Payoffs are

not significantly higher than in the Endogenous Help treatment for either type. In contrast, the

Commitment treatment leads to significantly higher minimum effort and effort levels in Rounds

21 – 30 than in either the No Help or Endogenous Help treatments. Payoffs for both types in the

final block are also significantly higher in the Commitment treatment than in the Endogenous

Help treatment. For low ability types, payoffs in both blocks are also significantly higher than in

the No Help treatment. As should be expected from Figure 8, the difference in high ability

payoffs between the Commitment and No Help treatments is never statistically significant.

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Conclusion 3: The Asymmetric Help treatment has a modest positive effect on effort and both

types’ payoffs. The Commitment treatment has a large persistent effect on effort. Compared

with the No Help treatment, help with commitment makes low ability types better off without

harming the high ability types. The data supports H3 for the Commitment treatment, but not for

the Asymmetric Help treatment.

Before discussing the Commitment treatment in detail, a few points are worth noting

about the Asymmetric Help treatment. Use of asymmetric help, while not the modal choice, was

far from rare. Asymmetric help was selected for 18% of the observations from Rounds 11 – 30

of the Asymmetric Help treatment, with 15 of 21 high ability types using asymmetric help at

least once. Given that no help was provided in 33% of the observations, asymmetric help was

used in slightly more than a quarter of the observations where a positive level of help was

provided. The likelihood of using asymmetric help changed little over time. There is a weak

tendency to use asymmetric help more frequently when the previous round’s minimum effort by

low ability types was relatively low. More interestingly, low ability types who provided less

effort than their peers in the previous round are significantly more likely to receive higher than

average help if asymmetric help is used. In other words, asymmetric help is used to improve the

incentives for laggards to increase their effort rather than punishing them. Use of asymmetric

help does not lead to better performance. We have run regression analysis paralleling the

specification shown in Table 4 on data from the Asymmetric help treatment. When an

independent variable is added for use of asymmetric help, the coefficient estimate indicates that

use of asymmetric help leads to significantly lower minimum effort by low ability types. Oddly,

employee-level regressions find that asymmetric help leads to lower effort by low ability types

regardless or whether they were helped less or more than their peers. Given that asymmetric

help isn’t very useful, it is unsurprising that performance in the Asymmetric Help treatment is

not much better than in the Endogenous Help treatment. Since the difference between these

treatments isn’t close to statistical significance, we are inclined to attribute the slight

improvement in the Asymmetric Help treatment to chance.

Turning to the Commitment treatment, the use of help by high ability types isn’t so

different between the Endogenous Help and Commitment treatments. The average level of help

is higher in the Commitment treatment (1.40 vs. 1.21) but not dramatically so. When high ability

types in the Commitment treatment are given the opportunity prior to the final block to change

26

the amount of they provide, the majority of them do so (12 of 20). The mistake of cutting help

for successfully coordinated firms once again crops up – of twelve firms coordinated at 40 in

Round 20, four cut help for the second block while none increase help.

The difference between the Endogenous Help and Commitment treatments is that forced

commitment gives time for groups to strongly converge to a new equilibrium in the first block

with help (Rounds 11 – 20). All five groups where help is increased for the final block had a

minimum effort of 20 or less in Round 20. Three of these five groups converged to the efficient

outcome in the final block. As in the Endogenous Help treatment, increasing help leads to higher

effort by low ability types. Of the seven groups where help is decreased for the final block, four

had all four employees choosing 40 in Round 20. Moreover, all employees in these firms had

been chosing 40 since at least Round 14. These groups had a firmly established norm of

coordinating on the efficient outcome. Two of the groups saw a brief decrease in Round 21, in

both cases due to a change by a single employee, but every employee in these four groups chose

effort level 40 in Rounds 22 – 30. Unlike the Endogenous Help treatment, a decrease in help in

the Commitment treatment does not cause a decrease in effort by the low ability types.

Intuitively, coordination games are all about beliefs. If everyone believes there will be

coordination failure, this becomes a self-fulfilling prophecy, and if everyone expects successful

coordination at the efficient outcome, this too tends to occur. Changing help has an effect at

least in part because it affects beliefs. However, if subjects have strongly converged to the

efficient equilibrium, this creates a precedent that has a larger impact on beliefs than a decrease

in help. The Commitment treatment gives the time for strong convergence to the efficient

equilibrium to occur before the high ability types can disrupt things by changing help.

Given the small (and statistically insignificant) difference between minimum efforts in

the Commitment and Exogenous Help treatments, it seems natural to conclude that the positive

effect of help in the Commitment treatment is almost entirely driven by changing the incentives

for low ability types rather than forward induction or reciprocity. However, we need to be

careful when comparing data from the Exogenous Help and Commitment treatments, since many

high ability types in the Commitment treatment offered less help than was imposed in the

Exogenous Help treatment and, unlike the Endogenous Help treatment, there is a strong

monotonic relationship between help and minimum effort in the Commitment treatment. Table 7

shows average minimum effort levels, broken down by five round blocks, for the Exogenous

27

Help treatment, the Commitment treatment, and for the subset of data from the Commitment

treatment where Employee 1 provided two units of help to each of the low ability types (i.e.

chose the level of help that was imposed in the Exogenous Help treatment).

Table 7: Exogenous vs Endogenous Help with Commitment

Exogenous Help Commitment (all data)

Commitment (H = 2)

Rounds 11-15 18.8 20.6 23.0 Rounds 16-20 23.4 25.9 27.0 Rounds 21-25 26.9 30.0 35.3 Rounds 26-30 29.4 31.3 36.8

For all rounds the average minimum effort is higher in the Commitment treatment than in

the Exogenous Help treatment, but the differences are modest. However, when we control for

incentives by only looking at observations with the same distribution of effort costs, the

difference between the two treatments widens substantially. This still underestimates the

differences for Rounds 21 – 30 since there is negative correlation between help in the final block

and minimum effort in the final round of the previous block (Round 20). Low ability types

receiving two units of help in the final block of the Commitment treatment tend to come from

groups with a history of previous coordination failure yet do especially well. If we run a

regression equivalent to those described in Appendix B and include controls for help, the

difference between the Commitment and Exogenous Help treatments is significant at the 10%

level for both Rounds 11 – 20 and Rounds 21 – 30. This suggests that the effect of endogenously

provided help is not solely due to changing the incentives to coordinate, but also reflects some

combination of forward induction and reciprocity.

A final question is whether changing beliefs or reciprocity is playing a greater role in

driving the effects of help on effort. While our experiments aren’t particularly intended (or

designed) to explore this issue, the data does give us some insights. The asymmetric response to

help documented for the Endogenous Help treatment is consistent with negative reciprocity

having a larger effect than positive reciprocity (Offerman, 2002), but can also be rationalized by

changing beliefs.13 Data from the Commitment treatment is more helpful, suggesting that the

13 Suppose subjects believe that distribution of increases in other subjects’ efforts following a positive change to help is identical to the the distribution of decreases in other subjects’ efforts following a negative change. Because the minimum function is driven by the lowest effort, they should therefore believe that minimum effort will decrease

28

effects of changing help are not due to reciprocity. Cutting help when the group has converged

to a positive effort level is at least as unkind in the Commitment treatment as in the Endogenous

Help treatment. Not only is the high ability type helping himself at the expense of low ability

types, he is doing so in a way that cannot be quickly reversed. If reciprocity was largely to

blame for the strong negative reaction to decreased help, we would expect more of a reaction in

the Commitment treatment when help is reduced for firms that have converged to the efficient

equilibrium.14 This isn’t conclusive, but arguments centering around beliefs are particularly

natural for coordination games and seem to fit the data better.

7. Final remarks The purpose of this paper is to study whether help from high ability employees to low

ability types is an effective tool for leading groups out of performance traps. The answer is a

qualified yes. Endogenously provided help leads to significant improvement in firm performance

if high ability types must commit to a level of help for an extended period of time.

Our work suggests that it is not sufficient for managers to encourage help among workers

(for example by forming work teams as in Hamilton et al). Management must also encourage

stability in how help is provided. This need not be overly complicated. Simply holding a

meeting on a monthly basis where employees discuss what they will do for the upcoming month,

including what help they will provide others, may serve as a useful device for fostering more

stable commitments to help. Keeping work groups together for an extended period of time rather

than re-matching workers also has the effect of creating a more stable environment where levels

of help are more likely to be steady.

One issue that our work does not address is endogenous commitment to help. In the

Endogenous Help treatment, high ability workers have no mechanism to commit that they will

not change the level of help in the future, while in the Commitment treatment they have no

choice but to keep the level of help fixed for an entire block. It would be useful to know if high

more following a decrease in help than minimum effort will increase following an increase in help. This asymmetric expectation about the effects of increases and decreases in help leads to the asymmetric response we observe in the data. If subjects correctly anticipate an asymmetric response to changes in help, this only reinforces the asymmetry. 14 Another possibility is that the negative reaction to decreasing help in the Endogenous Help treatment reflects strategic teaching by low ability types. Since help cannot be adjusted again, strategic teaching would not have an impact on effort if help is decreased prior to the final block in the Commitment treatment. The data does not support this explanation since the reaction to decreases in help in the Endogenous Help treatment is actually somewhat stronger in the Rounds 21 – 30 than in Rounds 11 – 20.

29

ability types would take advantage of a commitment device if one was offered but not required.

Our suspicion is that they would not – if subjects understood the value of commitment, they

probably wouldn’t be undercutting successful coordination in the first place – but the question is

ultimately an empirical one.

Finally, there is a broader point to be taken from our work. The experimental literature

on weak-link games has suggested a number of mechanisms that are useful for overcoming

coordination failure. We conjecture that the importance of commitment is not limited to the

effectiveness of help. Escaping from a performance trap is a gradual process, and one that can

be disrupted by negative changes along many dimensions. For example, in a companion paper

we examine the effects of commitment in turnaround games where a subject plays the role of

manager and sets the bonus. Initial results suggest that commitment plays an important positive

role in this setting as well. In general, a good strategy for individuals to follow in attempting to

escape from coordination failure is to pick an approach and stick with it. Even the best of

approaches will fail if used inconsistently.

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Camerer, Colin (2003), Behavioral Game Theory: Experiments in Strategic Interaction,

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Chadhuri, A., (2009), Experiments in Economics, Playing Fair with Money. Routledge: New

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Linear Models,” Biometrika, 73, 13-22.

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Moulton, Brent (1986), “Random Group Effects and the Prevision of Regression Estimates,”

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Science, 45, 804-823.

32

APPENDIX A INSTRUCTIONS FOR ENDOGENOUS HELP TREATMENT

INSTRUCTIONS IN ROUND 1

The purpose of this experiment is to study how people make decisions in a particular situation. The instructions are simple and if you follow them carefully you will confidentially receive an amount of money at the end of the experiment, since none of you will be informed about others’ earnings If you have a question, please raise your hand. Aside form these questions, any communication with other participants is not permitted and will lead to an immediate exclusion from the experiment.

1. Just for participating in the experiment you receive an initial payment of 2500 ECUs (a virtual monetary unit). This experiment will have several blocks of 10 rounds each. The conditions of the experiment are identical within each block and although some condition may change between blocks we will promptly inform you of any changes. In each round you will be part of the same group of 4 participants, the composition of which does not change during the whole experiment and which will call your firm. Given that nobody will know the identity of the members of each firm, all the decisions you make during the experiment will be absolutely anonymous.

2. As worker of your firm you have to decide how to split your working week of 40 working hours between Activity A and Activity B. Given that the hours that you do not assign to one activity are automatically assigned to the other one, we you will be asked to decide how many hours you devote to Activity A. Given that the available options are to devote 0, 10, 20, 30 or 40 to Activity A, this implies automatically devoting 40, 30, 20, 10 , 0 to Activity B (respectively).

3. In each round you will receive a base wage of 200 ECUs. Your earnings will depend on this base wage, on your decisions and on a bonus which is a function of the minimum number of hours devoted to Activity A by any member of the group. The bonus is chosen by the central server of the lab, which simulates the decisions of firm’s management. Before making any decision, you will receive the information about the value of the bonus.

4. Your earnings in each round depend on the hours that you devote to Activity A, on the number of hours devoted by the rest of the workers of your firm tu activity A, on the bonus chosen by management and on a Ce, a variable that represents the cost of your effort from working. Your earnings are given by the following formula:

Base wage -Effort + Bonus Earnings of worker = 200 -(Ce × Hi ) +(B × min(HA))

where Hi is the number of hours you devote to Activity A and min(HA) is the minimum number of hours that a worker of your firm devotes to Activity A.

5. In each firm there are two types of workers: 1 worker of type 1 and 3 workers of type 2. At the beginning of this session you will be informed about what type of worker you are for the whole experiment, since types will not change. The types of workers differ exclusively in their initial cost of effort, Ce, which for one type is higher than for the other. During the first 10 rounds:

a. The workers of type 1 have an effort cost of Ce equal to 1 and their earnings are given by the formula:

Earnings of type 1 = 200 − 1 × Hi + B × min(HA) b. The workers of type 2 have an effort cost of Ce equal to 9 and their earnings are given by the

formula: Earnings of type 2 = 200 − 9 × Hi + B × min(HA)

33

6. Although none of the participants will receive any payment as management of the firm, you will receive

information about firm profit, which depend on the hours devoted to Activity A by the workers of the firm and on the bonus B, according to the following formula (which you don’t need to memorize):

Firm profit = 100 + (52 − 4 × B) × min(HA)

7. In each round, the computer will show a similar table to the ones that are shown below. The payoffs that are shown adjust with the (variable) values of B. In the examples that follow we use B=8. Note that this information is shown in the top part of the payoff tables. For the players of type 1, with an effort cost of 1, the payoff table is:

B = 8

Firm profit = 100 + 20 × min(HA)

Minimum of hours devoted to actividad A by the other workers

0 10 20 30 40

My hours in activity A

0 200 200 200 200 200 10 190 270 270 270 270

20 180 260 340 340 340 30 170 250 330 410 410 40 160 240 320 400 480

For the players of type 2, with an effort cost of 9, the payoff table is:

B = 8

Beneficios empresa = 100 + 20 × min(HA)

Minimum of hours devoted to actividad A by the other workers

0 10 20 30 40

My hours in activity A

0 200 200 200 200 200 10 110 190 190 190 190 20 20 100 180 180 180 30 -70 10 90 170 170 40 -160 -80 0 80 160

34

8. Each worker chooses the number of hours devoted to activity A using buttons located on the right side of the screen. You can your choice as often as you want, but once you click the “OK” button, the decision will be final.

9. When you make your decision you will not know what the rest of the workers in your firm have done, but, after each round you will know the number of hours that the workers of your firm have devoted to Activity A, the profit of your firm, your earnings for the round and your accumulated earnings. You will have a summary of the results of previous rounds.

10. At the end of the experiment, your accumulated earnings in ECUs will be converted into euros at an exchange rate of 500 ECUs = €1.

Example Before starting the experiment, please go through the following questions. For each of the questions suppose that B=8 and that you are a type 1 worker, with an effort cost of 1. Using your payoff table which you have on the previous page suppose that you choose to devote 10 hours to Activity A and that the other workers of your firm decide to devote, 30, 20 and 40 hours to Activity A. In this case:

The minimum number that a worker devotes to Activity A is 10. Your earnings are 270 ECUs. Now consider that you are a type 2 worker with effort cost of 9. Your payoff table is the second one on the previous page. Suppose that you choose to devote 20 hours to Activity A and that the other workers of your firm decide to devote, 30, 20 and 40 hours to Activity A. In this case:

The minimum number that a worker devotes to Activity A is 20. Your earnings are 180 ECUs.

35

A short quiz Imagine that you are a type 1 worker (effort cost=1). Using your payoff table, suppose that you decide to devote 20 hours to Activity A. The other workers of your firm choose to devote 30, 0 and 10 hours to Activity A. The minimum number of hours that a worker of my firm devotes to A is_____ My earning in ECUs is________ Suppose that you decide to devote 0 hours to Activity A. The other workers of your firm choose to devote 20, 30 and 10 hours to Activity A. The minimum number of hours that a worker of my firm devotes to A is_____ My earning in ECUs is________ I am using in the same firm during the whole experiment: □ True. □ False My actions and payoffs are confidential: □ True. □ False. Imagine that you are a type 2 worker (effort cost=9). Using your payoff table, suppose that you decide to devote 20 hours to Activity A. The other workers of your firm choose to devote 30, 0 and 10 hours to Activity A. The minimum number of hours that a worker of my firm devotes to A is_____ My earning in ECUs is________ Suppose that you decide to devote 0 hours to Activity A. The other workers of your firm choose to devote 20, 30 and 10 hours to Activity A. The minimum number of hours that a worker of my firm devotes to A is_____ My earning in ECUs is________ I am using in the same firm during the whole experiment: □ True. □ False My actions and payoffs are confidential: □ True. □ False.

36

INSTRUCTIONS IN ROUND 11 AND 21 From this round on, there are two changes in the experiment: (i) the value of the bonus change to 14 and (ii) the type 1 worker of each group has the possibility to reduce the effort costs of the type 2 workers of his/her group, by increasing his/her own effort cost. The type 1 worker will make this decision before the effort decisions for each round are made. For each unit in which he/she reduces the cost of the 3 type 2 workers, the cost of the type 1 worker will go up by 3. The reduction will have to be the same for all type 2 workers of the group, so that the concrete options that you will have are the following:

Effort cost fo type 1 Effort cost for type 2 Help level of 0 1 9 Help level of 1 4 8 Help level of 2 7 7 Help level of 3 10 6 Help level of 4 13 5

37

The different possibilities of changing effort costs lead to different payoff tables. Given that the possible effort costs are 1, 4, 5, 6, 7, 8, 9, 10 and 13 in what follows we show the payoff tables for each of the possible effort costs. Ce = 1 B = 14 Firm profit = 100 + -4 × min(HA) Minimum of hours devoted to activity A by the other workers 0 10 20 30 40

0 200 200 200 200 200 My hours in activity A 10 190 330 330 330 330 20 180 320 460 460 460 30 170 310 450 590 590 40 160 300 440 580 720

Ce = 4 B = 14 Firm profit = 100 + -4 × min(HA) Minimum of hours devoted to activity A by the other workers 0 10 20 30 40

0 200 200 200 200 200 My hours in activity A 10 160 300 300 300 300 20 120 260 400 400 400 30 80 220 360 500 500 40 40 180 320 460 600

Ce = 5 B = 14 Firm profit = 100 + -4 × min(HA) Minimum of hours devoted to activity A by the other workers 0 10 20 30 40

0 200 200 200 200 200 My hours in activity A 10 150 290 290 290 290 20 100 240 380 380 380 30 50 190 330 470 470 40 0 140 280 420 560

38

Ce = 6 B = 14 Firm profit = 100 + -4 × min(HA) Minimum of hours devoted to activity A by the other workers 0 10 20 30 40

0 200 200 200 200 200 My hours in activity

A 10 140 280 280 280 280 20 80 220 360 360 360 30 20 160 300 440 440 40 -40 100 240 380 520

Ce = 7 B = 14 Firm profit = 100 + -4 × min(HA) Minimum of hours devoted to activity A by the other workers 0 10 20 30 40

0 200 200 200 200 200 My hours in activity

A 10 130 270 270 270 270 20 60 200 340 340 340 30 -10 130 270 410 410 40 -80 60 200 340 480

Ce = 8 B = 14 Firm profit = 100 + -4 × min(HA) Minimum of hours devoted to activity A by the other workers 0 10 20 30 40

0 200 200 200 200 200 My hours in activity

A 10 120 260 260 260 260 20 40 180 320 320 320

30 -40 100 240 380 380 40 -120 20 160 300 440

39

Ce = 9 B = 14 Firm profit = 100 + -4 × min(HA) Minimum of hours devoted to activity A by the other workers 0 10 20 30 40

0 200 200 200 200 200 My hours in activity

A 10 110 250 250 250 250 20 20 160 300 300 300 30 -70 70 210 350 350 40 -160 -20 120 260 400

Ce = 10 B = 14 Firm profit = 100 + -4 × min(HA) Minimum of hours devoted to activity A by the other workers 0 10 20 30 40

0 200 200 200 200 200 My hours in activity

A 10 100 240 240 240 240 20 0 140 280 280 280 30 -100 40 180 320 320 40 -200 -60 80 220 360

Ce = 13 B = 14 Firm profit = 100 + -4 × min(HA) Minimum of hours devoted to activity A by the other workers 0 10 20 30 40

0 200 200 200 200 200 My hours in activity

A 10 70 210 210 210 210 20 -60 80 220 220 220 30 -190 -50 90 230 230 40 -320 -180 -40 100 240

40

Appendix B: The regressions shown in Table B.1 provide a formal statistical backing for our

conclusions about the effects of the various treatments on subject choices. Models 1 and 1a look

at firm-level data with the minimum effort as the dependent variable while Models 2 and 2a look

at employee-level data with effort as the dependent variable. Given that these dependent

variables are ordered categories, use of an ordered probit specification is natural.15 Both data

sets include all observations from all five treatments for Rounds 11 – 30. Since there are four

employees per firm, Model 2 has four times as many observations as Model 1. The independent

variables include a dummy for Rounds 21 – 30 and interaction terms between treatment dummies

and dummies for Rounds 11 – 20 and Rounds 21 – 30. These interaction terms capture

differences between the treatment and the base for the time period in question. Models 1 and 1a

differ only in what treatment is used as the base – the No Help treatment in Model 1 and the

Endogenous Help treatment in Model 1a. Models 2 and 2a differ in the same manner.

Since there are multiple observations from each firm, correcting for firm effects is a

central issue in the regressions. We do this in a couple of ways. First, standard errors in both

regressions are corrected for clustering (Moulton, 1986; Liang and Zeger, 1986) at the firm

level.16 Second, even though effort level zero is the unique equilibrium choice in Rounds 1 – 10,

the majority of employees (57%) choose positive effort at least once in this first phase. We

therefore include several controls for behavior in Rounds 1 – 10 with the idea that these will pick

up an individual and/or group tendency to choose higher effort levels. Specifically we include

the firm’s average minimum effort in Rounds 1 – 10, the firm’s average total effort (sum of

effort over the four workers) in Rounds 1 -10, and, in the regressions on employee-level data, the

employee’s average effort over Rounds 1 – 10.

We start by looking at the statistical support for Conclusion 1. Looking at Models 1 and

1a, few significant differences are observed at the firm-level between the treatments in

Experiment 1. The only significant difference is between the Endogenous and Exogenous Help

treatments in Rounds 21 – 30, and this is only significant at the 10% level. Looking at

employee-level data, in Models 2 and 2a, even this difference fails to achieve statistical

significance. The regression results therefore support Conclusion 1 – endogenous help is doing 15 The cutoffs are not reported on Table 4 since they are of little economic interest. Copies of all regression output are available from the authors upon request. 16 In Models 2 and 2a, observations from individuals in the same firm are obviously not independent. We therefore cluster at the firm level rather than the employee level.

41

nothing to improve firm productivity (as measured by minimum effort) and even the positive

effect of exogenous help is modest.

Turning to Conclusion 3, the regression analysis reported in Table B.1 also supports this

conclusion. Compared with either the No Help or Endogenous Help treatments, the Asymmetric

Help treatment does not have a statistically significant effect on minimum effort or effort. In

contrast, the Commitment treatment leads to significantly higher minimum effort and effort

levels in Rounds 21 – 30. This effect is significant at the 10% level in Model 1 (barely missing

the 5% level) and at the 5% level for Models 2 – 4. If the regressions are altered so the base is

the Exogenous Help treatments, no significant differences are found between this treatment and

the Commitment treatment. As noted in the main text, differences are found if a control is added

for the amount of help provided.

42

Table B.1: Ordered Probit Regressions on Treatment Effects

Model 1 Model 1a Model 2 Model 2a Dependent Variable

Minimum Effort Firm Level

Minimum Effort Firm Level

Effort Employee Level

Effort Employee Level

Base Treatment No Help Endogenous Help No Help Endogenous Help

Rounds 21 – 30 .186 (.124)

.256**

(.103)-.035 (.135)

.054 (.104)

No Help * Rounds 11 – 20 .159

(.246) .085 (.227)

No Help * Rounds 21 – 30 .088

(.300) -.005 (.286)

Endogenous Help * Rounds 11 – 20

-.159 (.246) -.085

(.227) Endogenous Help * Rounds 21 – 30

-.088 (.300) .005

(.286) Exogenous Help * Rounds 11 – 20

.133 (.274)

.291 (.249)

.063 (.283)

.148 (.254)

Exogenous Help * Rounds 21 – 30

.448 (.353)

.536*

(.302).461

(.353).456

(.306)Asymmetric Help * Rounds 11 – 20

.009 (.253)

.167 (.227)

.090 (.240)

.175 (.208)

Asymmetric Help * Rounds 21 – 30

.175 (.327)

.263 (.273)

.281 (.319)

.277 (.269)

Commitment * Rounds 11 – 20

.302 (.308)

.461 (.288)

.293 (.304)

.377 (.279)

Commitment * Rounds 21 – 30

.715*

(.376) .803**

(.330).782**

(.378).778**

(.337)Ave. Min. Effort Rounds 1 – 10

.081**

(.038) .081**

(.038).090**

(.038)090**

(.038)Ave. Total Effort

Rounds 1 – 10 -.008 (.007)

-.008 (.007)

-.007 (.006)

-.007 (.006)

Average Effort, Rounds 1 – 10 .012***

(.003) .012***

(.003) Log

Likelihood -3401.69 -3401.69 -12910.00 -12910.00

Number of Observations 2400 2400 9600 9600

Notes: Standard errors are corrected for clustering at the firm level. Three (***), two (**), and one (*) stars indicate statistical significance at the 1%, 5%, and 10% respectively.

40

Figure 1: Effect of Help on Minimum Effort

30

35

25

um E

ffor

t

15

20

vera

ge M

inim

u

10

Av

0

5

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Period

No Help Exogenous Help Endogenous Help

550

Figure 2: Effect of Help on High Ability Type Payoffs

450

500

400

f (E

CU

s)

300

350

Aver

age

Payo

ff

250

A

150

200

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Period

No Help Exogenous Help Endogenous Help

450

Figure 3: Effect of Help on Low Ability Type Payoffs

350

400

300

f (E

CU

s)

200

250

Aver

age

Payo

ff

150

A

50

100

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Period

No Help Exogenous Help Endogenous Help

10

Figure 4: Effect of Changing Help on High Cost Type Effort (Rounds 12 ‐ 30)

74 b

6

8

pes

74 obs

2

4

, High Co

st Typ

45 obs

114 obs

204 obs34 b

‐2

0

Minim

um Effort, 45 obs

46 obs34 obs

22 obs 196 obs 6 obs

‐6

‐4

Chan

ge in

 M

‐8

6

‐10

0 10, 20, or 30 40Lagged Minimum Effort, High Cost Types

Decrease Help Constant Help Increase Help

60

Figure 5: Frequency of Changing Help, Minimum Effort, and High Ability Type Profits

509 obs

40

15 obs 6 obs

30

9 obs

10

20

0

10

0 ≤ Number of Changes ≤ 2 3 ≤ Number of Changes ≤ 6 7 ≤ Number of Changes ≤ 10 Number of Changes > 10

Frequency of Changing Help

Minimum Effort, Low Ability Types Average Payoff (divided by 10), High Ability Types

100%

Figure 6: Changing Help and the Lagged Minimum Effort of Low Ability Types

80%

60%

40%

20%20%

0%Lagged Minimum Effort = 0 Lagged Minimum Effort = 10, 20, or 30 Lagged Minimum Effort = 40

Decrease Help Constant Help Increase Help

40

Figure 7: Average Minimum Effort by Treatment

30

35

25

um E

ffor

t

15

20

vera

ge M

inim

u

10

Av

0

5

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Period

No Help Exogenous Help Endogenous Help Asymmetric Help Commitment

550

Figure 8: Average High Ability Type Payoffs by Treatment

450

500

400

f (E

CU

s)

300

350

Aver

age

Payo

ff

250

A

150

200

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Period

No Help Exogenous Help Endogenous Help Asymmetric Help Commitment

450

Figure 9: Average Low Ability Type Payoffs by Treatment

350

400

300

f (E

CU

s)

200

250

Aver

age

Payo

ff

150

A

50

100

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Period

No Help Endogenous Help Asymmetric Help Commitment Exogenous Help