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Returns-Based Beliefs and The Prisoner’s Dilemma

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  • Velu, C.
  • Iyer, S.

Abstract

Returns-based beliefs provides an explanation for the anomaly between the theory and empirics for the one-shot and finitely-repeated Prisoner’s Dilemma games. Even in a fully specified game, there is strategic uncertainty as players attempt to coordinate their actions. Therefore players form subjective probabilities of the actions of their opponents. We provide a new method termed the ‘returns-based beliefs’ approach of forming subjective probabilities that is based upon the expected returns of a particular strategy, in proportion to the total expected returns of all strategies. This method can be applied even in the absence of knowledge of the players’ respective histories.

Suggested Citation

  • Velu, C. & Iyer, S., 2008. "Returns-Based Beliefs and The Prisoner’s Dilemma," Cambridge Working Papers in Economics 0854, Faculty of Economics, University of Cambridge.
    • Handle: RePEc:cam:camdae:0854
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    1. Pedro Dal BÛ, 2002. "Cooperation Under the Shadow of the Future: Experimental Evidence from Infinitely Repeated Games," Working Papers 2002-20, Brown University, Department of Economics.
    2. Jacob K. Goeree & Charles A. Holt, 2001. "Ten Little Treasures of Game Theory and Ten Intuitive Contradictions," American Economic Review, American Economic Association, vol. 91(5), pages 1402-1422, December.
    3. Kreps, David M. & Milgrom, Paul & Roberts, John & Wilson, Robert, 1982. "Rational cooperation in the finitely repeated prisoners' dilemma," Journal of Economic Theory, Elsevier, vol. 27(2), pages 245-252, August.
    4. Cooper, Russell & DeJong, Douglas V. & Forsythe, Robert & Ross, Thomas W., 1996. "Cooperation without Reputation: Experimental Evidence from Prisoner's Dilemma Games," Games and Economic Behavior, Elsevier, vol. 12(2), pages 187-218, February.
    5. Ariel Rubinstein, 2006. "Dilemmas of an Economic Theorist," Econometrica, Econometric Society, vol. 74(4), pages 865-883, July.
    6. Joseph Farrell & Matthew Rabin, 1996. "Cheap Talk," Journal of Economic Perspectives, American Economic Association, vol. 10(3), pages 103-118, Summer.
    7. Ariel Rubinstein, 2007. "Instinctive and Cognitive Reasoning: A Study of Response Times," Economic Journal, Royal Economic Society, vol. 117(523), pages 1243-1259, October.
    8. Van Huyck, John B & Battalio, Raymond C & Beil, Richard O, 1990. "Tacit Coordination Games, Strategic Uncertainty, and Coordination Failure," American Economic Review, American Economic Association, vol. 80(1), pages 234-248, March.
    9. Joseph B. Kadane & Patrick D. Larkey, 1983. "The Confusion of Is and Ought in Game Theoretic Contexts," Management Science, INFORMS, vol. 29(12), pages 1365-1379, December.
    10. Andreoni, James A & Miller, John H, 1993. "Rational Cooperation in the Finitely Repeated Prisoner's Dilemma: Experimental Evidence," Economic Journal, Royal Economic Society, vol. 103(418), pages 570-585, May.
    11. Cooper, Russell, et al, 1990. "Selection Criteria in Coordination Games: Some Experimental Results," American Economic Review, American Economic Association, vol. 80(1), pages 218-233, March.
    12. Ernst Fehr & Simon Gächter, 2002. "Altruistic punishment in humans," Nature, Nature, vol. 415(6868), pages 137-140, January.
    13. Harsanyi, John C, 1978. "Bayesian Decision Theory and Utilitarian Ethics," American Economic Review, American Economic Association, vol. 68(2), pages 223-228, May.
    14. David Sally, 1995. "Conversation and Cooperation in Social Dilemmas," Rationality and Society, , vol. 7(1), pages 58-92, January.
    15. Janssen, Marco A., 2008. "Evolution of cooperation in a one-shot Prisoner's Dilemma based on recognition of trustworthy and untrustworthy agents," Journal of Economic Behavior & Organization, Elsevier, vol. 65(3-4), pages 458-471, March.
    16. Robert J. Aumann & Jacques H. Dreze, 2008. "Rational Expectations in Games," American Economic Review, American Economic Association, vol. 98(1), pages 72-86, March.
    17. Rosenthal, Robert W., 1981. "Games of perfect information, predatory pricing and the chain-store paradox," Journal of Economic Theory, Elsevier, vol. 25(1), pages 92-100, August.
    18. Adam Brandenburger & Eddie Dekel, 2014. "Rationalizability and Correlated Equilibria," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 3, pages 43-57, World Scientific Publishing Co. Pte. Ltd..
    19. Martin Shubik, 1969. "Game Theory, Behavior and the Paradox of the Prisoners Dilemma -- 3 Solutions," Cowles Foundation Discussion Papers 274, Cowles Foundation for Research in Economics, Yale University.
    20. Reny Philip J., 1993. "Common Belief and the Theory of Games with Perfect Information," Journal of Economic Theory, Elsevier, vol. 59(2), pages 257-274, April.
    21. John C. Harsanyi, 1982. "Comment---Subjective Probability and the Theory of Games: Comments on Kadane and Larkey's Paper," Management Science, INFORMS, vol. 28(2), pages 120-124, February.
    22. Pedro Dal Bó, 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.
    23. Rabin, Matthew, 1993. "Incorporating Fairness into Game Theory and Economics," American Economic Review, American Economic Association, vol. 83(5), pages 1281-1302, December.
    24. Roth, Alvin E & Schoumaker, Francoise, 1983. "Expectations and Reputations in Bargaining: An Experimental Study," American Economic Review, American Economic Association, vol. 73(3), pages 362-372, June.
    25. Herbert Simon, 1956. "A comparison of game theory and learning theory," Psychometrika, Springer;The Psychometric Society, vol. 21(3), pages 267-272, September.
    26. Adam Brandenburger, 2007. "The power of paradox: some recent developments in interactive epistemology," International Journal of Game Theory, Springer;Game Theory Society, vol. 35(4), pages 465-492, April.
    27. Basu, Kaushik, 1990. "On the Non-existence of a Rationality Definition for Extensive Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(1), pages 33-44.
    28. Ariel Rubinstein, 2007. "Instinctive and Cognitive Reasoning: Response Times Study," Levine's Bibliography 321307000000001011, UCLA Department of Economics.
    29. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
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    More about this item

    Keywords

    Prisoner’s Dilemma; Rationality; Subjective Probabilities; Returns-Based Beliefs.;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection

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