Cheap Threats Cheap Talk in the Prisoners Dilemma with Peer Punishment Joseph Guse Neville Fogarty

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

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

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? Questions 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…

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).

6. Contribution Results from BPP (2005) 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):

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

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)

10. Average Cooperation By Round and Treatment Round

11. Average Punishment Spending By Round and Treatment Round

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

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

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

15. A Cooperation Regression(subject fixed effects)

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.

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.

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?

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.

20. Selfish Updater’s Problem

21. Selfish Updater’s Best Response

22. Many Do Not Fit Neatly:Approximate Selfish Updater 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.

23. Subject 7: Vengeful Cooperator

24. S16: Committed Defector or Selfish Updater?

25. Some are Very Strange • Punishes on ALL 4 PD outcomes! • Need new type: Sadistic Random Cooperater. • The best I can say: wacky punishment behavior declines over time.

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?