The impact of the termination rule on cooperation in a prisoner’s dilemma experiment

Cooperation in prisoner's dilemma games can usually be sustained only if the game has an infinite horizon. We analyze to what extent the theoretically crucial distinction of finite vs. infinite-horizon games is reflected in the outcomes of a prisoner's dilemma experiment. We compare three different experimental termination rules in four treatments: a known finite end, an unknown end, and two variants with a random termination rule (with a high and with a low continuation probability, where cooperation can occur in a subgame-perfect equilibrium only with the high probability). We find that the termination rules do not significantly affect average cooperation rates. Specifically, employing a random termination rule does not cause significantly more cooperation compared to a known finite horizon, and the continuation probability does not significantly affect average cooperation rates either. However, the termination rules may influence cooperation over time and end-game behavior. Further, the (expected) length of the game significantly increases cooperation rates. The results suggest that subjects may need at least some learning opportunities (like repetitions of the supergame) before significant backward induction arguments in finitely repeated game have force.

[1]  Ulrich Kamecke,et al.  Infinity in the lab. How do people play repeated games? , 2012 .

[2]  Justus Haucap,et al.  Consumer Behavior towards On-net/Off-net Price Differentiation , 2011 .

[3]  Werner Güth,et al.  Finitely repeated prisoners’ dilemma experiments without a commonly known end , 2012, Int. J. Game Theory.

[4]  Charles A. Holt,et al.  An Experimental Test of the Consistent-Conjectures Hypothesis , 1985 .

[5]  Howard Raiffa,et al.  Games and Decisions: Introduction and Critical Survey. , 1958 .

[6]  Annika Herr,et al.  Quality and Welfare in a Mixed Duopoly with Regulated Prices: The Case of a Public and a Private Hospital , 2011 .

[7]  R. Axelrod.  More Effective Choice in the Prisoner's Dilemma , 1980 .

[8]  Klaus Gugler,et al.  How Effective is European Merger Control , 2011 .

[9]  David M. Kreps,et al.  Rational cooperation in the finitely repeated prisoners' dilemma , 1982 .

[10]  Vijay Krishna,et al.  Finitely Repeated Games , 1985 .

[11]  Stefan Haigner,et al.  The first shall be last: serial position effects in the case contestants evaluate each other , 2010 .

[12]  Achim Hauck,et al.  The euro area interbank market and the liquidity management of the eurosystem in the financial crisis , 2010 .

[13]  Hans-Theo Normann,et al.  A Within-Subject Analysis of Other-Regarding Preferences , 2010, Games Econ. Behav..

[14]  Dale O. Stahl,et al.  The graph of Prisoners' Dilemma supergame payoffs as a function of the discount factor , 1991 .

[15]  W. Güth,et al.  Can Subgame Perfect Equilibrium Threats Foster Cooperation? An Experimental Test of Finite‐Horizon Folk Theorems , 2013 .

[16]  R. Selten,et al.  End behavior in sequences of finite prisoner's dilemma supergames , 1986 .

[17]  A. Rapoport,et al.  Prisoner's Dilemma , 1965 .

[18]  J. Kagel,et al.  Handbook of Experimental Economics , 1997 .

[19]  W. Hamilton,et al.  The Evolution of Cooperation , 1984 .

[20]  Werner Güth,et al.  When does the game end? Public goods experiments with non-definite and non-commonly known time horizons , 2005 .

[21]  Jim Engle-Warnick,et al.  The evolution of strategies in a repeated trust game , 2004 .

[22]  Tobias Wenzel,et al.  Transparency, price-dependent demand and product variety , 2011 .

[23]  L. G. Morehous.  One - play, two - play, five - play, and ten-play runs of Prisoner's Dilemma 1 , 1966 .

[24]  Ralf Dewenter,et al.  Calling Party Pays or Receiving Party Pays? The Diffusion of Mobile Telephony with Endogenous Regulation , 2005 .

[25]  Alvin E. Roth,et al.  Equilibrium behavior and repeated play of the prisoner's dilemma , 1978 .

[26]  U. Fischbacher.  z-Tree: Zurich toolbox for ready-made economic experiments , 1999 .

[27]  Alvin E. Roth,et al.  Expecting Continued Play in Prisoner's Dilemma Games , 1983 .

[28]  Werner Güth,et al.  Voluntary Cooperation Based on Equilibrium Retribution - An Experiment Testing Finite-Horizon Folk Theorems , 2009 .

[29]  John H. Miller,et al.  Rational Cooperation in the Finitely Repeated Prisoner's Dilemma: Experimental Evidence , 1993 .

[30]  L. Samuelson.  A note on uncertainty and cooperation in a finitely repeated prisoner's dilemma , 1987 .

[31]  P. Bó.  Cooperation under the Shadow of the Future: Experimental Evidence from Infinitely Repeated Games , 2005 .

[32]  Gary E. Bolton,et al.  ERC: A Theory of Equity, Reciprocity, and Competition , 2000 .

[33]  Douglas A. Wolfe,et al.  Nonparametric Statistical Methods , 1973 .

[34]  Christian Wey,et al.  On the role of consumer expectations in markets with network effects , 2012 .

[35]  V. Krishna,et al.  Nash equilibria of finitely repeated games , 1987 .

[36]  A. Neyman.  Cooperation in Repeated Games When the Number of Stages is not Commonly Known , 1999 .

[37]  Hans-Theo Normann,et al.  Vertical Mergers, Foreclosure and Raising Rivals' Costs – Experimental Evidence , 2011 .

[38]  M. M. Flood.  Some Experimental Games , 1958 .

[39]  Tobias Wenzel,et al.  Deregulation of Shopping Hours: The Impact on Independent Retailers and Chain Stores , 2011 .

[40]  Thomas A. Husted,et al.  An Experimental Test of Discount-Rate Effects on Collusive Behaviour in Duopoly Markets , 1993 .

[41]  Mehmet Karaçuka,et al.  Competition in Turkish mobile telecommunications markets: Price elasticities and network substitution , 2011 .

[42]  J. Potters,et al.  Bertrand colludes more than Cournot , 2007 .

[43]  Klaus M. Schmidt,et al.  A Theory of Fairness, Competition, and Cooperation , 1999 .

[44]  D. Wolfe,et al.  Nonparametric Statistical Methods. , 1974 .

[45]  Tobias Wenzel,et al.  Getting beer during commercials: Adverse effects of ad-avoidance , 2011, Inf. Econ. Policy.

[47]  R. Selten,et al.  Duopoly Strategies Programmed by Experienced Players , 1997 .

[48]  A. Rapoport,et al.  Prisoner's Dilemma: A Study in Conflict and Co-operation , 1970 .

[49]  H. Orzen.  Counterintuitive number effects in experimental oligopolies , 2008 .