Effect of Cheap Talk in Peer Punishment Game
Explore the impact of cheap talk in a peer punishment game by studying threatening and promising behaviors in the Prisoner's Dilemma context. Investigate if cheap talk leads to increased cooperation and more effective punishments.
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Cheap Threats Cheap Talk in the Prisoners Dilemma with Peer Punishment Joseph Guse Neville Fogarty Washington & Lee University April 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? Questions and Background 3
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). 5
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 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. 6
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): C D C (own) 42 14 D (own) 63 21 7
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 0.9 0.8 Coop (NT) 0.7 0.6 Coop (T) 0.5 0.4 0.3 0.2 0.1 0 0 1 2 3 4 5 6 7 8 9 10 Round 11 12 13 14 15 16 17 18 19 10
Average Punishment Spending By Round and Treatment 4 3.5 Punish (NT) 3 Punish (T) 2.5 2 1.5 1 0.5 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Round 11
To Punish or Not Did Punish ? by PD Outcome (% of Obs) No Talk Treatment Did Punish? by PD Outcome (% of Obs) Talk Treatment cc cd dc dd cc cd dc dd 39.7 34.3 Last 18 Rounds X 18 Subjects = 324 Observations Last 18 Rounds X 20 Subjects = 360 Observations 30.3 18.8 148 Non-Zero Spending Choices 9.6 90 Non-Zero Spending Choices 10 12.7 10.2 4 8.1 3.9 9 5.8 "Per "Perverse 1.1 1.5 1.1 Normal Zero Zero Non-zero Non-Zero Spending Decision Spending Decision Results: Descriptive Stats: Punishment 12
How Much To Punish? No Talk Non-Zero Punishment Spending Decisions by Outcome (%) No Talk Treatment cc cd dc dd 22 of 324 4 Unique Subjects (10,6,3,3) 32 out of 324 (9.9%) 7 Unique Subjects 11,6,6,4,2,2,1 6.8 9.9 0.6 1.2 0.6 1.9 0.9 1.2 0.3 0.6 0 0.3 0.6 0.6 0.3 0 0 0.3 0 0 0 0 0 0 0 0 0 0 0.3 0 0 0 0.3 0 0.3 0 0 0.3 0 0 0.3 0 0 0 1 0 0 2 0 0 0 3 0 4 0 0 5 0 6 0 7 0 8 0 9 10 11 12 13 14 Spending Choice Results: Descriptive Stats: Punishment 13
How Much To Punish? w/ Talk Non Zero Punishment Spending Choices (%) Talk Treatment cc cd dc dd 8.6 31 of 360 (8.6%) 6.4 10 of 360 6 Unique Subjects (3,3,1,1,1,1) 4.4 4.4 3.3 7 of 360 (1.9%) 5 Unique Subjects 2.5 2.8 2.2 0.8 0.6 0 0.6 0 0.3 0.3 0.3 0 0.3 0 0 0.3 0 0 0.3 0 0 0 0 0.3 0 0 0.3 0 1.9 0 0 0 0 0 0 0 0 0 1 0 0 0 2 0 0 0.3 3 0 0 4 0 5 0 6 0 7 0 8 0 9 10 11 12 13 14 Spending Choice Results: Descriptive Stats: Punishment 14
A Cooperation Regression (subject fixed effects) ownCoop otherCoop_L1 otherCoop_L2 otherCoop_L3 otherCoop_L4 otherPunish_L1 X DC_L1 cc_L1 Coef. -0.03333 0.033284 0.023296 0.01555 t-stat -0.64 0.87 0.62 0.43 0.003484 0.238576 0.59 2.7 15
(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
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
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
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
Many Do Not Fit Neatly: Approximate Selfish Updater 12's History round 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 part 8 15 2 9 10 7 2 0 11 9 8 14 15 9 1 5 11 15 1 17 ownCoop 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 othCoop 1 1 1 1 0 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 ownPun 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 othPun 14 0 14 14 0 14 14 2 0 0 4 0 3 14 0 0 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. 22
Subject 7: Vengeful Cooperator 7's History round 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 part 13 16 1 4 8 12 5 9 10 8 1 3 8 4 16 10 17 13 9 15 ownCoop 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 othCoop 0 0 1 0 1 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 ownPun 14 14 0 14 0 14 0 0 14 14 0 0 14 0 14 14 14 14 14 14 othPun 0 5 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 23
S16: Committed Defector or Selfish Updater? 16's History round 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 part 5 7 5 10 17 17 4 17 8 2 5 11 6 5 7 11 10 11 14 4 ownCoop 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 othCoop 0 1 1 1 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 ownPun 12 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 othPun 5 14 0 0 0 0 0 0 0 0 0 0 0 0 14 0 0 0 0 0 24
Some are Very Strange 0's History round 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Punishes on ALL 4 PD outcomes! Need new type: Sadistic Random Cooperater. The best I can say: wacky punishment behavior declines over time. part 9 1 13 17 15 8 15 12 9 5 6 15 13 17 4 17 5 9 3 13 ownCoop 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 1 1 0 1 0 othCoop 1 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 ownPun 2 3 4 5 3 7 5 2 6 3 2 3 1 3 4 0 1 2 1 0 othPun 0 14 0 6 0 0 3 0 0 0 3 3 0 0 0 0 0 0 0 0 25
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
