An Experiment on Trust in Triads

Werner Raub

Workshop on Social Theory, Trust, Social Networks, and Social Capital II

National Chengchi University – NCCUApril 2011

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Trust by Example I

July 18, 2007: end date to purchase a copy of the first edition of Theory of Games and Economic Behavior by John von Neumann and Oskar Morgenstern at eBay from the seller “bibliomonster” for US-$ 1,900.00. The item had a fixed price listing (eBay’s “Buy It Now” option) and could only be purchased without bidding in an auction. Item description: “Bound in original publishers red cloth a bit rubbed at head of spine. Black (ink?) mark on top board. Minor shelf wear, else very good. Internally, clean and free of ink, marginalia and soiling. No dogeared pages or tears. Includes the often missing corrigenda leaf. A nice, collectable copy.”

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Trust by Example II

• A potential buyer at eBay has to decide whether to buy the rare first edition of a book offered by a seller and to send the money

• The seller, after receiving the money, has to decide whether or not to ship the book to the buyer

• If the seller ships and the book corresponds with the specifications, both buyer and seller are happier after the deal than before the deal

• If the seller does not ship the book, he can try to sell it again, while the buyer has lost her money

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The Trust Game

Trustee/Seller

Trustor/Buyer

No trust Trust

HonorAbuse

1

2

R

R1

2

S

T1

2

P

P

S1 < P1 < R1

P2 < R2 < T2

No trust Trust

Abuse Honor

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Outline

1. Theory and hypotheses on embedded trust

2. Design of the experiment

3. Results

4. Related findings from other empirical studies using complementary research designs

5. Conclusions: ongoing and future research

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Theory and Hypotheses onEmbedded Trust

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Embedded Trust

• Trust problems (and other social and economic interactions) are often “embedded” in the sense of

• repeated transactions between the same actors

• actors encounter and exchange information with partners of their partner

need to extend predictions for trust situations to embedded settings (“trust in networks”)

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Embeddedness Mechanisms

Dyadicembeddedness

Networkembeddedness

Learning Common history of past interactions:information about the partner from own experiences

Information from third parties about their past experiences with the partner

Control Expected future interactions:opportunities for conditional cooperation via, e.g., “tit for tat”

Opportunities for conditional cooperation involving third parties: “voice” (reputation effects)

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Approach

• We distinguish between different embeddedness effects

• theoretically• empirically

• We consider “games on networks” and neglect “strategic network formation”: embeddedness is exogenous in the experiment (but see concluding discussion)

• We focus on trust as a result of “enlightened self-interest” and neglect (more or less) “non-selfish utility”

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Theories for Deriving Hypotheses on Embeddedness Effects

Dyadicembeddedness

Network embeddedness

Learning Adaptive learning models;information diffusion models

Learning and control

Models for repeated games with incomplete information

Control Models for repeated games with complete information

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Trust in Finitely Repeated Games with Incomplete Information: Intuition I

• Consider a finitely repeated Trust Game with a trustee who, with some positive (and possibly very small) probability, has no incentive to abuse trust in a one-shot Trust Game (e.g., “inequity aversion”)

• The trustee may then honor trust for one of two very different reasons:

1. No incentive to abuse trust in a one-shot Trust Game

2. Reputation building: if trust is abused, trustor can infer trustee’s type for sure (learning) and may never place trust again (control)

• Trustor may therefore be inclined to place trust

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Trust in Finitely Repeated Games with Incomplete Information: Intuition II

• Thus:

1. Trustor tries to learn about and controls the trustee, taking the trustee’s incentives for reputation building into account

2. Trustee balances long-term effects of his reputation and short-term incentives for abusing trust, taking into account that the trustor anticipates this balancing

• Some properties of the equilibrium:

1. Trust is placed and honored in “early” rounds of the game

2. Actors randomize afterwards

3. Placed trust is abused in “final” rounds of the game

4. Once abused, trust is never placed again

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Hypotheses – Summary

Dyadicembeddedness

Networkembeddedness

Learning

Trust increases (decreases) with positive (negative) own experiences with the trustee

Trust increases (decreases) with positive (negative) information on the trustee received from other trustors

Control Trust and trustworthiness increase with the likelihood of future interactions

Trust and trustworthiness increase with the trustor’s control opportunities through her network with other trustors

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Design of the Experiment

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Lab Experiment

• Subjects play repeated Trust Games in the lab

• Anonymous interactions with actual other subjects in the lab

• Complete game structure provided in the instructions; no deception

• Points earned represent actual money for the subjects

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Trust Game in the Lab Experiment

Number of points

A B

down

down

right

right A 10 10

B 0 40

20 20

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Interaction Structure

• Two trustors play with the same trustee for 15 rounds (“triads”)

• In each round, trustor 1 plays first, trustor 2 second

• Depending on experimental condition: information exchange about past behavior between trustors

Trustor 2

Trustee

Trustor 1

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Two Experimental Conditions

• No information exchange between trustors:each trustor only knows what happens in her own Trust Games with the trustee opportunity for dyadic learning and control no opportunity for network learning and control

• Full information exchange between trustors:after each Trust Game, also the trustor not involved in that game receives information on the choices made in that game opportunity for dyadic learning and control opportunity for network learning and control

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Further Set-Up

• Both conditions: subjects know what kind of information everybody receives

• Each subject plays three repeated trust games in the same information condition: once as trustor 1, once as trustor 2, once as trustee

• Subjects are rematched between the repeated games; never rematched to other subjects they had already played with; subjects are informed on the rematching process

• Experiment conducted in ELSE lab of UU, using z-Tree software

• 72 subjects, i.e., data on 72 triads and 72x15x2 = 2160 Trust Games (1080 with and 1080 without information exchange between trustors)

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Lab Experiment andEmbeddedness Effects

Lab experiment allows to test hypotheses on effects of dyadic embeddedness and network embeddedness on trust and trustworthiness

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Results

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Three-Level Logistic Regression

• Estimate probability to trust / honor trust conditional on past experiences, rounds to go, information condition

• Three-level random effects model:• Levels: decision – trustor – triad

• 2160 decisions by 144 trustors in 72 triads

• 1542 decisions by 72 trustees in 72 triads

• Clustering within trustors in different series of games neglected

• Trustor level variance is small

• Results are rather robust for the specification of random

structure

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Results: Effects of Embeddedness on Trust of the Trustor

.2.4

.6.8

1Pro

port

ion t

rust

0 5 10 15 Round

no info full info

144 trustors

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Results: Effects of Dyadic Embeddedness on Trust of the Trustor

Support for hypotheses on dyadic learning and on dyadic control effects on trustor behavior:

Trustors are more (less) likely to trust…

• after having experienced more honored (abused) trust in own interactions with trustee (dyadic learning)

• the larger (smaller) the number of rounds still to be played (also: strong endgame effect) (dyadic control)

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Results: Effects of Network Embeddedness on Trust of the Trustor

• Evidence for network learning effects on trustor behavior: trustors are more (less) likely to trust after having observed more honored (abused) trust in the other trustor’s interactions with the trustee

• No evidence for network control effects on trustor behavior: no main effect of information condition; no interaction effect of information condition with rounds still to be played; decrease of trust does not start later in condition with full information exchange between trustors

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Results: Effects of Embeddedness onTrustworthiness of theTrustee

.2.4

.6.8

1Pro

port

ion h

onore

d t

rust

0 5 10 15Round

no info full info

72 trustees

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Results: Effects of Dyadic Embeddedness on Trustworthiness of the Trustee

Support for hypothesis on dyadic control effects on trustee behavior:

• Trustees are more likely to honor trust the larger the number of rounds still to be played with the respective trustor

• Also: strong endgame effect

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Results: Effects of Network Embeddedness on Trustworthiness of the Trustee

Support for hypothesis on network control effects on trustee behavior:

• Positive effect of full information condition on likelihood of honoring trust

• Endgame effect stronger for interactions with trustor 2 (who has less control opportunities than trustor 1)

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Puzzle

• Trustee reacts to trustor’s opportunities for• dyadic control and• network controlTrustee seemingly takes reputation effects

of his behavior into account

• Trustor reacts to her own opportunities for dyadic control

• Trustor does not react to her own opportunities for network control

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Related Findings from Other Empirical Studies Using Complementary

Research Designs

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Evidence on Embeddedness Effects from Complementary Research Designs

• Approach: use complementary research designs (survey, vignette study, lab experiment) for multiple tests of the same hypotheses (cf.: triangulation, cross validation)

• Similar perspective:• Sociology: J.H. Goldthorpe (1996) The

Quantitative Analysis of Large-scale Data Sets and Rational Action Theory: For a Sociological Alliance, ESR 12

• Economics: G.W. Harrison & J.L. List (2004) Field Experiments, JEL 42(4)

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Alternative Designs:Advantages and Disadvantages

Advantages Disadvantages

Survey Actual interactions Measurement problems; less control over variables

Lab experiment

Control over incentives and embeddedness variables

Abstract; external validity

Vignette study

Less abstract than lab experiments; control over variables

Hypothetical interactions; lack of “incentive compatibility”

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Summary of Empirical Evidence

SurveyVignette

studyLab

experiment

Dyadiclearning • Consistent support for dyadic learning

and control effects on trust of trustor• Quite some support for dyadic control

effects on trustworthiness of trusteeDyadiccontrol

Network learning

• Consistent support for network learning effects on trust of trustor

• No support for network control effects on trust of trustor

• Consistent support for network control effects on trustworthiness of trustee

Networkcontrol

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Once Again the Puzzle

• Trustee reacts to trustor’s opportunities for• dyadic control and• network controlTrustee seemingly takes reputation effects

of his behavior into account

• Trustor reacts to her own opportunities for dyadic control

• Trustor does not react to her own opportunities for network control

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How (not) to Explain the Puzzle?

• Data and/or measurement problems (including sample selectivity and endogeneity of network embeddedness) could be (part of) the reason why we do not find network control effects on trustor behavior in survey data (see Buskens 2002)

• Data and/or measurement problems are much less plausible reasons for the lack of network control effects on trustor behavior in the experiment

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How to Explain the Puzzle:Limits of Strategic Rationality?

• General idea: Trustor anticipation on her own opportunities for network control involves too many steps of iterated reasoning, at least for inexperienced subjects

• Network control effects on trustee behavior require only that trustee anticipates that own present behavior affects future trust of the present or other trustors

• Network control effects on trustor behavior require that trustor anticipates that the trustee anticipates on effects of his present behavior on future trust of other trustors

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Similar Arguments in the Literature

• Equilibrium behavior becomes less likely when actors have to reason many steps ahead

• Equilibrium behavior requires that actors are sufficiently “experienced”

(see, e.g., Binmore, Camerer, Kreps)

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Conclusions:Ongoing and Future Research

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Testable Implications ofthe Explanation of the Puzzle and

Empirical Evidence

• In the experiment, trustors who have been in the role of trustee in an earlier game (and thus have more experience) should be more likely to react to network control opportunities. There is some support for this effect in our data.

• We also find support for network control effects on trustor behavior in one of our vignette studies with experienced subjects (purchase managers) in the trustor role.

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Extended Version of Our Experiment: Some Preliminary Evidence for Experience Effects I

• We meanwhile repeated the experiment with subjects playing 6 rather than 3 repeated trust games

• Each subject was twice in each role (trustor 1, trustor 2, trustee)

• 138 subjects, data on 8.280 trust games• First question: is there evidence for

experience effects in the sense that behavior in later repeated trust games differs from behavior in earlier repeated trust games?

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Extended Version of Our Experiment: Some Preliminary Evidence for Experience Effects II

0.2

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0 5 10 15 0 5 10 15

0 1

no network full network

Pro

port

ion

of p

lace

d tr

ust i

n tr

eat

me

nt 1

,2,3

and

4,5

,6

Period

Graphs by firsthalf

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Related Empirical Evidence fromOther Research

• Professionals tend to implement relatively complex equilibrium behavior as well as equilibrium behavior that requires quite some iterated reasoning, also in situations where non-professionals fail to do so:

• Professional soccer players (versus college students) in zero-sum games such as penalty kicks (but also strategically equivalent lab experiments): Palacios-Huerta & Volij; Berger & Hammer

• Chess Grandmasters versus college students in the Centipede Game: Palacios-Huerta & Volij

• Related empirical evidence on “spillover effects” between games (Bednar et al.)

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Further Extension: Investments in Embeddedness and Strategic Network

Formation I• Embeddedness is exogenous in the

experiment• Consider an alternative scenario: before

playing the repeated Trust Games, subjects themselves decide to play in one of the two information exchange conditions. Playing in “full information exchange between trustors” is costly

• Thus, the alternative scenario includes strategic network formation: subjects can invest in network embeddedness

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Further Extension: Investments in Embeddedness and Strategic Network

Formation II• The alternative scenario allows for an

analysis of strategic network formation under the assumption of full strategic rationality

• Questions:• Effects of game parameters (payoffs, # of

rounds of the repeated trust game)?• Effects of “who can invest in network

embeddedness (trustors or trustee)?”

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Further Extension: Investments in Embeddedness and Strategic Network

Formation III• Theoretical approach

• Calculate expected payoffs in equilibrium for the two conditions (“no information exchange between trustors” vs. “full information exchange between trustors”)

• Difference = willingness to pay• Issue: possible signaling effects if trustee

can invest in embeddedness

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Thanks for your attention!

More information:

www.fss.uu.nl/soc/iscore

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Additional Slides

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Further Details on the Experiment

• Sessions took between 55 and 70 minutes.• Subjects’ earnings

• Average: € 10.67

• € 10.25 in condition without

information exchange

• € 11.10 in condition with full

information exchange

• Minimum earnings: € 7.00

• Maximum earnings: € 12.40

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Comparison of the Design with Bolton et al. 2004 (BKO 04) and Bolton &

Ockenfels 2009 (B&O 09)

• “No information exchange between trustors” resembles the “partners market” in BKO 04 and B&O 09

• “Full information exchange between trustors” combines dyadic embeddedness and network embeddedness and thus differs from the “reputation market” in BKO 04 and B&O 09 that represents exclusively a form of network embeddedness

• BKO 04 and B&O 09 has no condition that combines dyadic and network embeddedness

• Our experiment neglects the “strangers market” in BKO 04 and B&O 09

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Trust Problems as Social Dilemmas

• The buyer (trustor) has to trust the seller (trustee) that he ships the book and that the book corresponds with the specifications

• The trustee has an incentive to abuse trust

• This may induce the trustor not to place trust in the first place

• Placed and honored trust is better for both actors than no trust.

• Hence, trust problems as an example of social dilemmas: goal-directed behavior leads to ‘poor’ outcomes (‘unintended consequences’)

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Trust Problems as a Sociological Problem

• Problem of social order

• Trust problems in economic exchange: (e.g., buyer-supplier, R&D-alliances)

• Trust problems in social exchange (e.g., help among friends)

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Results: Effects on Trust

Information condition No net effect

Abused own trust in past −

Honored own trust in past +

Abused other trust in past −

Honored other trust in past +

Rounds to go +

Rounds to go × information 0

Round 14 −

Round 15 −

Info cond × round 14 0

Info cond × round 15 −

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Results: Effects on Trustworthiness

Information condition +

Rounds to go +

Rounds to go × information −

Round 14 −

Round 15 −

Info cond × round 14 × trustor 2 −

Info cond × round 15 × trustor 2 −

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Results: Effects on Trust

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Results: Effects on Trustworthiness

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Results: Experience Effects