1. Cheap Threats Cheap Talk in the Prisoners Dilemma with Peer Punishment Joseph Guse Neville Fogarty Washington & Lee University April 29, 2010 1

2. Outline Questions and Background The Game Preliminary Results – The Data – Descriptive Statistics Cooperation Behavior Punishment Behavior Signaling Behavior – Regression Analysis (Sucks) – Typological Analysis 2

3. 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

4. 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

5. 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). 5

6. Contribution Results from BPP (2005) PeriodBasePFFFFwPCRCRwPNCTNCTwP 16.296.9610 9.339.426.576.43 101.946.107.818.945.218.751.955.84 6 Base = No Communication, No Punishment P and “wP” = Punishment Treatments: Price is.25 for all FF = 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.

7. 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 CD C (own) 4214 D (own) 6321

8. 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

9. 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

10. Average Cooperation By Round and Treatment 10 Round

11. Average Punishment Spending By Round and Treatment 11 Round

12. To Punish or Not 12Results: Descriptive Stats: Punishment

13. How Much To Punish? – No Talk 13Results: Descriptive Stats: Punishment

14. How Much To Punish? w/ Talk 14Results: Descriptive Stats: Punishment

15. A Cooperation Regression (subject fixed effects) ownCoopCoef.t-stat otherCoop_L1-0.03333-0.64 otherCoop_L20.0332840.87 otherCoop_L30.0232960.62 otherCoop_L40.015550.43 otherPunish_L1 X DC_L10.0034840.59 cc_L10.2385762.7 15

16. (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. 16

17. 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. 17

18. 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? 18

19. Candidate Typology for PD with Punishement SPE-Player: Always Defect, Never Punish a. honest: promises to defect b. dishonest Cooperator: Always cooperate no matter experience a.i. vengeful, honest a.ii vengeful, dishonest b.i. no vengeful, honest b.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. 19

20. Selfish Updater’s Problem 20

21. Selfish Updater’s Best Response 21

22. Many Do Not Fit Neatly: Approximate Selfish Updater 12's History roundpartownCoopothCoopownPunothPun 0801514 1150100 2201014 39010 4100000 5701014 62010 700002 8110000 991100 1081004 11140000 12150003 13901014 10000 1550000 16111080 17150000 1810000 19170000 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. 22

23. Subject 7: Vengeful Cooperator 7's History roundpartownCoopothCoopownPunothPun 01310140 11610145 211100 3410 0 481100 51210140 651100 791100 81010140 9810 0 1011100 1131100 12810144 1341100 141610140 151010140 161710140 171310140 18910140 191510140 23

24. S16: Committed Defector or Selfish Updater? 16's History roundpartownCoopothCoopownPunothPun 0510125 1701514 250100 3100100 4170000 5 0100 640000 7 0100 880000 920000 1050000 11 0000 1260100 1350000 147010 15110000 16100000 17110000 18140000 1940000 24

25. Some are Very Strange 0's History roundpartownCoopothCoopownPunothPun 091120 1101314 2130140 3170056 4151030 581170 6 0053 7120020 891160 950030 1061023 11150033 12131010 170030 1440140 15171000 1651010 1790020 1831010 19130000 Punishes on ALL 4 PD outcomes! Need new type: Sadistic Random Cooperater. The best I can say: wacky punishment behavior declines over time. 25

26. 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? 26