Cheap ThreatsCheap Talk in the Prisoners Dilemma with Peer Punishment

Joseph GuseNeville Fogarty

Washington & Lee UniversityApril 29, 2010

1

Outline• Questions and Background• The Game• Preliminary Results

– The Data– Descriptive Statistics

• Cooperation Behavior• Punishment Behavior• Signaling Behavior

– Regression Analysis (Sucks)– Typological Analysis

2

Questions

• What is the effect of Cheap Talk in a Peer Punishment game?– Does threatening to punish non-cooperative

behavior make punish more likely?– Do subjects make credible promises / threats?– Does Cheap Talk lead to more cooperation?

3Questions and Background

Background

• Many have looked at the effect of peer-punishment in social dilemma games (e.g. Prisoners Dilemma, Public Goods Games)Main Result: punishment works (so do rewards) well but not perfectly

• Many have looked at the effect of cheap talk in similar environments.

• Few studies at the intersection of cheap talk and punishment. Only one that we know of…

4

Bochet, Page and Putterman (2005)“Communication and Punishment in Voluntary Contribution Experiments”

• 8 Treatments (2 Punishment X 4 communication)• Basic Set-up:• Slightly strange quasi-repeated interactions. • Standard VCM. Marginal return = .4• Communication Treatments:

– Face to Face (FF)– Chat Room (CR). Monitored messages for obscenities,

identity revelation, etc.– Numerical Cheap Talk (NCT).

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Contribution Results from BPP (2005)

Period Base P FF FFwP CR CRwP NCT NCTwP

1 6.29 6.96 10 10 9.33 9.42 6.57 6.43

10 1.94 6.10 7.81 8.94 5.21 8.75 1.95 5.84

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Base = No Communication, No PunishmentP and “wP” = Punishment Treatments: Price is .25 for allFF = Face to Face Communication (No anonymity)CR = Electronic Chat Room (Anonymous)NCT = Numerical Cheap Talk (Anonymous)

Source: Bochet, Page and Putterman (2005), “Communication and Punishment in Voluntary Contribution Experiments”, Brown University Working Paper.

NOTE: Strange Order Effects. Punishment always enhances talk.Talk added to Punishment is NOT always good.

Our Game• Talk Treatment:

– Communication Stage: State your (reduced strategy),• PD Action in {C,D}• 4 Punishment Threats – one for each PD outcome.

– Prisoner’s Dilemma Stage (PD)– Punishment Stage

• Price = 1/3. • Cannot spend more than PD Earnings. Binding?

• No Talk Treatment (Control): same as above without talk stage.• Payoffs (in tokens) =

PD Earnings – (Own Punishment Spending) – 3*(Other Punishment Spending)– PD Earnings (symmetric):

7

C DC (own)

42 14

D (own)

63 21

Our Game (Cont)

• Random and Anonymous Matching in Each of 20 Rounds• Paid 50 cents per token on one round selected randomly from

last 18. (Publicly performed dice-roll)• Subjects were paid game earnings plus $5 show-up fee.• Implemented in “Labworks” written in Java using RMI.

– Pro: pure Java, reasonably fast.– Con: RMI communication is limited to subnet

8

Preliminary Data

• 684 Observations (38 Subjects X 20 Rounds)– 1 session of Talk with 20 subjects– 1 session of No-Talk with 18 subjects

• Primarily Undergrads with occasional Law and Staff• Run in Huntley Hall using Mobile Laptop Cart• Weekday Evenings• Typical Duration: 75 minutes (all inclusive)

9

Average Cooperation By Round and Treatment

10

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 190

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Coop (NT) Coop (T)

Round

Average Punishment Spending By Round and Treatment

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0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 190

0.5

1

1.5

2

2.5

3

3.5

4

Punish (NT)

Punish (T)

Round

To Punish or Not

12

ZeroNon-Zero

9

1.5

10.2 12.7

18.8

4

34.3

9.6

Did Punish ? by PD Outcome (% of Obs)No Talk Treatment

cc cd dc dd

Spending Decision

Nor-mal Pun-ish-ment

"Perverse"Pun-ishment

Last 18 Rounds X18 Subjects =324 Observations

90 Non-Zero Spending Choices

ZeroNon-zero

1.11.1

8.15.8

10

3.9

39.7

30.3

Did Punish? by PD Outcome (% of Obs)Talk Treatment

cc cd dc dd

Spending Decision

"Perverse Punish-ment"

Last 18 RoundsX 20 Subjects= 360 Observations

148 Non-ZeroSpending Choices

Results: Descriptive Stats: Punishment

How Much To Punish? – No Talk

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1 2 3 4 5 6 7 8 9 10 11 12 13 14

0.30 0 0.3 0.3 0.3 0.3

0 0 0 0 0 0 0

1.20.6 0.6

0 0 0 0 0.30 0 0 0 0

9.9

1.2

0 0.61.9

0.30 0 0 0 0 0 0 0 0

0.6 0.6

6.8

0.3 0.90.3

0 0 0 0 0 0 0 0

Non-Zero Punishment Spending Decisions by Outcome (%)No Talk Treatment

cc cd dc dd

Spending Choice

32 out of 324 (9.9%)7 Unique Subjects11,6,6,4,2,2,1

22 of 3244 Unique Subjects(10,6,3,3)

Results: Descriptive Stats: Punishment

How Much To Punish? w/ Talk

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1 2 3 4 5 6 7 8 9 10 11 12 13 14

0.3 0.30 0 0.3

0 0 0 0 0.30 0 0 0

0.60.3 0.3

2.2

0 0.3 0.30 0 0 0 0 0

1.9

0 00.8

0.3

2.8

0 0 0 0 0 0 0 0 0

4.4 4.4

6.4

3.3

2.5

0.6

8.6

0 0 0 0 0 0 0

Non Zero Punishment Spending Choices (%)Talk Treatment

cc cd dc dd

Spending Choice

7 of 360 (1.9%)5 Unique Subjects

10 of 3606 Unique Sub-jects(3,3,1,1,1,1)

31 of 360 (8.6%)7 Unique Sub-jects(17,4,3,3,2,1,1)

Results: Descriptive Stats: Punishment

A Cooperation Regression(subject fixed effects)

ownCoop Coef. t-statotherCoop_L1 -0.03333 -0.64otherCoop_L2 0.033284 0.87otherCoop_L3 0.023296 0.62otherCoop_L4 0.01555 0.43otherPunish_L1 X DC_L1 0.003484 0.59cc_L1 0.238576 2.7

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(This) Regression Analysis Sucks

• Estimating Effect of RHS variable on AVERAGE behavior.• Heterogenous Types:

– People have different preferences– Different ways and rates of learning– Different prior beliefs

• Subject Fixed Effects Regressions only admit limited heterogeneity: just estimates individual intercepts, not slopes – much less different functional forms.

• Example: Two subjects: one who reacts to punishment with guilt and regret, one with anger:– Punishment is important. – Coefficient (even with FE) is garbage.

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Typological Analysis

• Develop a Typology – a list of utility functional forms and/or parameter space(s).

• Fit Each Subject to a type and estimate parameters• Re-iterate typology: minimize types and parameters while

maintaining good fit.• What to do with this…

– Estimate Population Distribution.– Run Simulations.

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Typological Analysis II:Simulation Exercises

• Change Type/Parameter Value Distribution• Change Initial Beliefs• Sample Questions

• Which distributions sustain perfect cooperation?• The importance of initial beliefs?• Path Dependence?

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Candidate Typology for PD with Punishement

• SPE-Player: Always Defect, Never Punisha. honest: promises to defectb. dishonest

• Cooperator: Always cooperate no matter experiencea.i. vengeful, honesta.ii vengeful, dishonestb.i. no vengeful, honestb.ii not vengeful, dishonest

• Conditional/Reciprocal Cooperator: Initially cooperative, but turns to defection after getting screwed too many times. Formally the utility function would place some positive value on cooperation per se and negative value on being the "chump”. Similar possibilities for vengefulness and honesty as type 2.

• Selfish Updater: Cooperates or Defects based on experience with punishment and signals of punishment, never punishes. Formally only cares about monetary payoff and constructs best response based on current beliefs about others. Beliefs are updated each round. Heterogeneity of initial beliefs possible.

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Selfish Updater’s Problem

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Selfish Updater’s Best Response

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Many Do Not Fit Neatly:Approximate Selfish Updater

12's Historyround part ownCoop othCoop ownPun othPun

0 8 0 1 5 141 15 0 1 0 02 2 0 1 0 143 9 0 1 0 144 10 0 0 0 05 7 0 1 0 146 2 0 1 0 147 0 0 0 0 28 11 0 0 0 09 9 1 1 0 0

10 8 1 0 0 411 14 0 0 0 012 15 0 0 0 313 9 0 1 0 1414 1 0 0 0 015 5 0 0 0 016 11 1 0 8 017 15 0 0 0 018 1 0 0 0 019 17 0 0 0 0

• It would take a convoluted utility function to rationalize this behavior perfectly

• Selfish Updater works OK• A good SU should have

experimented in round 7 or 14 not 9 and 15.

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Subject 7: Vengeful Cooperator7's History

round part ownCoop othCoop ownPun othPun0 13 1 0 14 01 16 1 0 14 52 1 1 1 0 03 4 1 0 14 04 8 1 1 0 05 12 1 0 14 06 5 1 1 0 07 9 1 1 0 08 10 1 0 14 09 8 1 0 14 0

10 1 1 1 0 011 3 1 1 0 012 8 1 0 14 413 4 1 1 0 014 16 1 0 14 015 10 1 0 14 016 17 1 0 14 017 13 1 0 14 018 9 1 0 14 019 15 1 0 14 0

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S16: Committed Defector or Selfish Updater?

16's Historyround part ownCoop othCoop ownPun othPun

0 5 1 0 12 51 7 0 1 5 142 5 0 1 0 03 10 0 1 0 04 17 0 0 0 05 17 0 1 0 06 4 0 0 0 07 17 0 1 0 08 8 0 0 0 09 2 0 0 0 0

10 5 0 0 0 011 11 0 0 0 012 6 0 1 0 013 5 0 0 0 014 7 0 1 0 1415 11 0 0 0 016 10 0 0 0 017 11 0 0 0 018 14 0 0 0 019 4 0 0 0 0

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Some are Very Strange0's History

round part ownCoop othCoop ownPun othPun0 9 1 1 2 01 1 0 1 3 142 13 0 1 4 03 17 0 0 5 64 15 1 0 3 05 8 1 1 7 06 15 0 0 5 37 12 0 0 2 08 9 1 1 6 09 5 0 0 3 0

10 6 1 0 2 311 15 0 0 3 312 13 1 0 1 013 17 0 0 3 014 4 0 1 4 015 17 1 0 0 016 5 1 0 1 017 9 0 0 2 018 3 1 0 1 019 13 0 0 0 0

• Punishes on ALL 4 PD outcomes!

• Need new type: Sadistic Random Cooperater.

• The best I can say: wacky punishment behavior declines over time.

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The Larger Question

• We may be able to think of punishment and communication mechanism as inputs in some “cooperation production function”.

• What is rate of technical substitution?• Specifically, Can we maintain a fixed level of cooperation by

increasing the price of punishment (or rewards) and lowering barriers to communication?

• Can we answer this with sufficient experimental data and simulations?

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