Asymmetry helps to overcome the “diffusion of responsibility”

Punitive preferences, monetary incentives and tacit coordination in the punishment of defectors promote cooperation in humans

Andreas DiekmannETH Zurich

(with Wojtek Przepioka, Univ. of Utrecht)

16th Social Dilemma Conference,Hong Kong, June 22-25

Sanctioning Dilemma

N bystander. Who is readyto punish the norm violator?

(One bystander is sufficientfor punishment.)

Second orderfree rider problem

Sanctioning Dilemma

N bystander. Who is readyto punish the norm violator?

(One bystander is sufficientfor punishment.)

Sanctioning Dilemma

N bystander. Who is readyto punish the norm violator?

(One bystander is sufficientto punish a noisy free rider.)

Volunteer’s DilemmaThe Volunteer’s Dilemma is a N-player binary choice game (for N ≥ 2) with a step-level production function. A player can produce a collective good at cost K > 0. When the good is produced, each player obtains the benefit U > K > 0. If no player volunteers, the good is not produced and all players receive a payoff 0.Example: “Bystander intervention in emergencies” (Darley & Latane 1968)

0 1 2 … N - 1 other C-Players

C U - K U - K U - K … U - K

D 0 U U … U U > K > 0

No dominant strategy, but N asymmetric pure equilibria in which one player volunteers while all other defect. Cf. Diekmann (1985).Moreover, another equilibrium in mixed strategies with symmetric payoffs.

► Actor’s choice is “defection”: Actor receives U if at least one other player is cooperative and 0 otherwise.

► Actor’s choice is “cooperation”: Actor receives U – K with certainty.

► This is a non-linear PGG with a step level production of the collective good.

There are many other examples of a volunteer‘s dilemma in:

► Sociology, social psychology (bystander effect and diffusion of responsibility)Economics (e.g. innovations and patent rights) etc.Computer sciences (decentralized computer networks)Traffic communication systems etc.

► Biologists found numerous situations corresponding to a volunteer‘s dilemma inrecent years (mammals defending a territory, alarm calls, many examples of microorganisms, Archetti 2009a,b, 2010 etc.)

► Interesting example from evolutionary biology: „Invertase (an enzym that splits sugar molecules AD) in yeast are public goods (= U) because they are diffused outside the cell; their production is costly (= K), but their lack, if nobody produces them, can be lethal“ (= 0), Archetti 2009, see Gore et al. 2009)

► „Some other cases have been classified as snowdrift game (SG), although in factthey are also volunteer‘s dilemmas because they do not involve pairwise interactions“ (Archetti 2009)

► „saccharomyces cerevisiae“: „Invertase in yeast are public goods (= U) because they are diffused outside the cell; their production is costly (= K), but their lack, if nobody produces them, can be lethal“ (= 0), Archetti 2009, see Gore et al. 2009)

► There would be no beer without the Volunteer‘s Dilemma of „saccharomyces cerevisiae“!

http://www.google.de/imgres?imgurl=http%3A%2F%2Fwww.allmystery.de%2Fi%2Ft8c050d_121001_merkel_bier_dpa_buettner_g.jpg&imgrefurl=http%3A%2F%2Fwww.allmystery.de%2Fthemen%2Fuh95228-229&h=433&w=600&tbnid=4rNid4FhNbs1HM%3A&zoom=1&docid=10kb-CBQ648GbM&hl=de&ei=ZNIqVZf_EcGMsgH444P4Dg&tbm=isch&iact=rc&uact=3&dur=1262&page=8&start=215&ndsp=31&ved=0CFcQrQMwGzjIAQ

Cooperation in symmetric

game

► p = 1 - N-1√ K/U

“Diffusion of responsibility

effect”

►Asymmetric Game with

one “strong” and N-1 “weak”

actors Us-Ks < U - K

►Pure strategy equilibrium:

p = 1 for strong and p = 0

for weak actors.

Model Prediction: Equilibrium Strategy

Diekmann, A., 1985. Volunteer‘s Dilemma, Journal of Conflict Resolution 29.1993. Cooperation in an Asymmetric Volunteer's Dilemma Game. Intern. J. of Game Theory 22.

Asymmetric Volunteer’s Dilemma (VOD)

• Heterogeneity of costs and gains: Ui, Ki for i = 1, …, N; Ui > (Ui – Ki) > 0

• Special case: A “strong” cooperative player receives Us – Ks , N-1 symmetric “weak” players’ get U – K whereby:

Us – Ks > Uw – Kw > 0

• Strategy profile of an “asymmetric”, efficient (Pareto optimal) Nash equilibrium:

► s = (Cs, D, D, D, D, …,D)

• I.e. the “strong player” is the volunteer (the player with the lowest cost and/or the highest gain). All other players defect.

► In the asymmetric dilemma: Exploitation of the strong player by the weak actors.

►Paradox of mixed Nash equilibrium: The strongest player is the least likely to take action!

Cooperation:

►Rational solution of the asymmetric game. Follows from axioms of Harsanyi/Selten theory

PLoS one August 2014

► s = (Cs, D, D, D, D, …,D)

► strong player cooperates, weak players free ride is stable ESS

Our Experiment with the symmetric and asymmetric volunteer‘s dilemma (VOD) as an alternative model for the sanctioning problem:

Hypotheses:

1. Actors execute self-interested, strategic punishment. Assumption of „punitive“ preferences is not necessary.

2. Higher punishment rate in the asymmetric situation. We expect strategic punishment in the symmetric and the asymmetric game. The proportion that the cheater will be punished is higher in the asymmetric situation than in the symmetric situation.

3. Efficiency. The rate of „efficient“ punishment (no waste of punishment costs), i.e. exactly one actor punishes is higher in the asymmetric compared to the symmetric situation.

4. Deterrence. With a punishment option the rate of norm violations will be larger in the symmetric than in the asymmetric situation.

Player X (the potential wrongdoer) decides eitherto violate or to stick to a norm. The violation of the norm hurts players A, B, C(a negative externality).

Players A, B, C have the possibility to punishnorm violations. A, B, C are in a VOD situation.

One player is sufficient to sanction X on cost Kthereby restoring the norm (production of the collectivegood U > K). In more detail:

The strategic situation

• A single actor is sufficient to punish a norm violation.• Sanctioning is costly (K) and restores the social norm. Both,

sanctioning and free riding victims of a norm violation profit (U) with U > K.

• Groups of four consisting of player X and three other players A, B, C. Players have an endowment of 100 MUs in each round.

• X has the option to steal 50 from each of the other players A,B,C. If he steals he will get 250 = 100 + 150 while A,B,C have 100 each. Distribution: (250, 100, 100, 100)

• However, A, B, C have a veto right. A veto costs 25 and X is obliged to pay the stolen money back. For example, B and C veto (and no extra punishment for X) results in the following distribution:

(100, 150, 125, 125).• Penalty for X varies in treatments: 1. No penalty, 2. Penalty = 60.

Example: Endowment 100. X steals. A vetoes, penalty of 60, K=25. Resulting distribution: X = 40, A = 125, B = 150, C = 150

Norm violation: X steals 150► Ui = 50

Number of subjects 48 48 48 48

1. Symmetric game

N = 3 „victims“, collective good U = 50, veto costs K = 25

Individual cooperation:Mixed Nash-equilibrium: P(cooperation) = 1- (N-1)√ K/U = 1 - √ 25/50 = 0.29

Collective good production:Probability that at least one player vetoes: 1 – (1-0.29)3 = 0.65

Efficient production of collective good:Probability that exactly one player vetoes: 3 ∙ 0.29 ∙ 0.712 = 0.44

2. Asymmetric game

N = 3 victims, veto costs of „weak“ players 35, veto cost of „strong“ player 25.

Nash-equilibrium prediction: P(cooperation strong player) = 1 P(cooperation weak player) = 0.

Two further conditions: Symmetric and asymmetric game

Cooperation (sanctioning) in the Volunteer‘s Dilemma

• VOD: U > K > 0

1. symmetric

2. asymmetric• MHD: K > U > 0

3. symmetric

4. asymmetric

►Homo oeconomicus prediction: zero probability of cooperation (sanctioning)!

►Cooperation in MHD is altruistic punishment!

Missing-Hero Dilemma. Strategic self-interest versus altruistic punishment

Cooperation (sanctioning) in the Missing Hero Dilemma

Chimpanzees solve an asymmetricvolunteer‘ dilemma.

Groups of three. One actor (operating the action box in room 3) is sufficient to produce the collective good U (orange juice In room 1). The cooperative player has costs K because he has to move from (3) to (1) and might get asmaller amount of juice than free riders.

(1) (2)

(3)

Schneider, Melis, Tomaselli (2012)

High ranked(strong) actorscooperate while weak actorsfree ride (highrank = 1, lowrank = 3.)

Foto: Süddeutsche Zeitung, 5.4.13

High rank

„Dominant individual pushes at the action box and then travels to the trough areawhere a second individual

is already drinking.“ (Schneider et al. 2012. 3-troughs condition.) Videoclip by courtesy of A. Schneider. Here, this is shown by dominant chimp: Jahaga.

Results

• Peer punishment and solution of second-order dilemma due to strategic self-interest.

• Asymmetry promotes efficient cooperation.• Results in VOD are very much in accordance with game

theory models.• However, in contrast to predictions of game theory and in

accordance with „negative reciprocity“ there is a moderate degree of altruistic punishment (20 %) in the MHD

• and a very high degree of altruistic punishment (62 %) in the asymmetric MHD.

• Strong actors are exploited in single rounds by the weak in the VOD as well as in the MHD.

► Asymmetry counteracts the diffusion of

responsibility – even in a MHD

The End

May 2015

2013

May 2015

References:

► Please, send an e-mail to: adiekmann@ethz.ch if you are interested in the papers or download from Research Gate.

1.

2.

Peer-Punishment

• Many collective good problems are not adequately modeled by the linear public good game.

• Often, one person is sufficient to punish norm violations.• The punishing actor profits, albeit not as much as free riders (K <

U).• Under these conditions, the sanctioning dilemma („second-order

free rider dilemma“) is a volunteer‘s dilemma. • Then we have „strategic“ punishment instead of „altruistic“

punishment and the assumption of ‚punitive preference‘ is no longer necessary.

• However, there is „diffusion of responsibility“ in a symmetric game. Asymmetry counteracts this effect and promotes cooperation – As a deterrent a certain stick helps more than a diffuse stick.

• Strong actors cooperate in the asymmetric dilemma – exploitation of the strong by the weak!

Winkelried in the battle of Sempach, 1386

Aus Wikipedia

Experiment in our computer lab DeSciL

Online march 27, 2013

Individual level cooperation

Prediction (Nash equilibrium strategy): 0.345 strong: p = 1, weak: p = 0

symmetric asymmetric

At least one victim vetoes(punishment of cheater)Symmetric, predicted 0.72Asymmetric, predicted 1

Exactly one victim vetoes(efficient punishment)Symmetric, predicted 0.44Asymmetric, predicted 1

► Low penalty in asymmetric situation has the same effect as high penaltyin the symmetric situation

Deterrence: Offender‘s stealing rate

Stealing Rate of Actor X

Note: In the symmetric condition stealing drops by 58 percent pointsIf there is a penalty of 120. In the asymmetric condition the rate dropsBy 59 percent points with a penalty of 40. the deterrence effect of asymmetryIs three times the size of the penalty.

Stealing Rate of Actor X

Note: In the symmetric condition stealing drops by 58 percent pointsIf there is a penalty of 120. In the asymmetric condition the rate dropsBy 59 percent points with a penalty of 40. The deterrence effect of asymmetryIs three times the size of the penalty.

Penal120 40

• Whelan (1997) provides an example from ancient politics which is analyzed in terms of collective good theory:

• As the Greek polis’ had been under threat by the Persian emperor Darius in the fifth century B.C. Athens was the volunteer to resist the Persian attack while other Greek states such as Sparta defected.

• The collective good of Greek independence was preserved by the victory of Athens at Marathon.

• In this historical example, the strategic interactions of states resemble an asymmetric volunteer’s dilemma.

• About sixty polis had an interest not being colonized by the Persians.

• Most of them defected while Athens, the most powerful state, was almost alone to act in the common interest.

Asymmetry and Cooperation