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Cooperation, but no reciprocity: Individual strategies in the repeated Prisoner's Dilemma

  • Breitmoser, Yves

A recent advance in our understanding of repeated PDs is the detection of a threshold d* at which laboratory subjects start to cooperate predictively. This threshold is substantially above the classic threshold "existence of Grim equilibrium" and has been characterized axiomatically by Blonski, Ockenfels, and Spagnolo (2011, BOS). In this paper, I derive its behavioral foundations. First, I show that the threshold is equivalent to existence of a "Semi-Grim" equilibrium s_cc>s_cd=s_dc>s_dd. It is cooperative (s_cc>0.5), non-reciprocal (s_cd=s_dc), and robust to imperfect monitoring ("belief-free"). Next, I show that the no-reciprocity condition s_cd=s_dc also follows from robustness to random-utility perturbations (logit equilibrium). Finally, I re-analyze strategies in four recent experiments and find that the majority of subjects indeed plays Semi-Grim when it is an equilibrium strategy, which explains d*'s predictive success.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 41731.

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Date of creation: 04 Oct 2012
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Handle: RePEc:pra:mprapa:41731
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  1. John Duffy & Jack Ochs, 2004. "Cooperative Behavior and the Frequency of Social Interaction," Levine's Working Paper Archive 122247000000000060, David K. Levine.
  2. Yves Breitmoser & Jonathan H.W. Tan & Daniel John Zizzo, 2008. "Understanding Perpetual R&D Races," Discussion Papers 2008-04, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
  3. Kandori, Michihiro, 2002. "Introduction to Repeated Games with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 1-15, January.
  4. Doraszelski, Ulrich & Escobar, Juan, 2010. "A theory of regular Markov perfect equilibria in dynamic stochastic games: genericity, stability, and purification," Theoretical Economics, Econometric Society, vol. 5(3), September.
  5. Choi, Syngjoo & Gale, Douglas & Kariv, Shachar, 2008. "Sequential equilibrium in monotone games: A theory-based analysis of experimental data," Journal of Economic Theory, Elsevier, vol. 143(1), pages 302-330, November.
  6. Johannes Hörner & Wojciech Olszewski, 2006. "The Folk Theorem for Games with Private Almost-Perfect Monitoring," Econometrica, Econometric Society, vol. 74(6), pages 1499-1544, November.
  7. Jim Engle-Warnick & Robert L. Slonim, 2001. "Inferring Repeated Game Strategies From Actions: Evidence From Trust Game Experiments," Economics Papers 2001-W13, Economics Group, Nuffield College, University of Oxford.
  8. Pedro Dal Bo & Guillaume R. Frochette, 2011. "The Evolution of Cooperation in Infinitely Repeated Games: Experimental Evidence," American Economic Review, American Economic Association, vol. 101(1), pages 411-29, February.
  9. Pedro Dal B�, 2005. "Cooperation under the Shadow of the Future: Experimental Evidence from Infinitely Repeated Games," American Economic Review, American Economic Association, vol. 95(5), pages 1591-1604, December.
  10. Fudenberg, Drew & Yamamoto, Yuichi, 2010. "Repeated Games Where the Payoffs and Monitoring Structure Are Unknown," Scholarly Articles 13411374, Harvard University Department of Economics.
  11. Jacob K. Goeree & Charles A. Holt & Thomas R. Palfrey, 2000. "Quantal Response Equilibrium and Overbidding in Private-Value Auctions," Virginia Economics Online Papers 345, University of Virginia, Department of Economics.
  12. Imhof, Lorens & Nowak, Martin & Fudenberg, Drew, 2007. "Tit-for-Tat or Win-Stay, Lose-Shift?," Scholarly Articles 3200671, Harvard University Department of Economics.
  13. Jeffrey C. Ely & Johannes Horner & Wojciech Olszewski, 2003. "Belief-free Equilibria in Repeated Games," Levine's Working Paper Archive 666156000000000367, David K. Levine.
  14. Engle-Warnick, Jim & Slonim, Robert L., 2004. "The evolution of strategies in a repeated trust game," Journal of Economic Behavior & Organization, Elsevier, vol. 55(4), pages 553-573, December.
  15. Srihari Govindan & Robert Wilson, 2006. "Sufficient Conditions for Stable Equilibria," Levine's Bibliography 784828000000000267, UCLA Department of Economics.
  16. Rand, David G & Fudenberg, Drew & Dreber, Anna, 2012. "Slow to Anger and Fast to Forgive: Cooperation in an Uncertain World," Scholarly Articles 11223697, Harvard University Department of Economics.
  17. Barlo, Mehmet & Carmona, Guilherme & Sabourian, Hamid, 2009. "Repeated games with one-memory," Journal of Economic Theory, Elsevier, vol. 144(1), pages 312-336, January.
  18. R. McKelvey & T. Palfrey, 2010. "Quantal Response Equilibria for Normal Form Games," Levine's Working Paper Archive 510, David K. Levine.
  19. Breitmoser, Yves, 2012. "Strategic reasoning in p-beauty contests," Games and Economic Behavior, Elsevier, vol. 75(2), pages 555-569.
  20. Johannes Hörner & Stefano Lovo, 2009. "Belief-Free Equilibria in Games With Incomplete Information," Econometrica, Econometric Society, vol. 77(2), pages 453-487, 03.
  21. Matthias Blonski & Peter Ockenfels & Giancarlo Spagnolo, 2011. "Equilibrium Selection in the Repeated Prisoner's Dilemma: Axiomatic Approach and Experimental Evidence," American Economic Journal: Microeconomics, American Economic Association, vol. 3(3), pages 164-92, August.
  22. Lisa Bruttel & Ulrich Kamecke, 2012. "Infinity in the lab. How do people play repeated games?," Theory and Decision, Springer, vol. 72(2), pages 205-219, February.
  23. Goeree, Jacob K. & Holt, Charles A. & Laury, Susan K., 2002. "Private costs and public benefits: unraveling the effects of altruism and noisy behavior," Journal of Public Economics, Elsevier, vol. 83(2), pages 255-276, February.
  24. Sabourian, Hamid, 1998. "Repeated games with M-period bounded memory (pure strategies)," Journal of Mathematical Economics, Elsevier, vol. 30(1), pages 1-35, August.
  25. Fey, Mark & McKelvey, Richard D & Palfrey, Thomas R, 1996. "An Experimental Study of Constant-Sum Centipede Games," International Journal of Game Theory, Springer, vol. 25(3), pages 269-87.
  26. C. Monica Capra, 1999. "Anomalous Behavior in a Traveler's Dilemma?," American Economic Review, American Economic Association, vol. 89(3), pages 678-690, June.
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