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Equilibrium Play and Best Response to (Stated) Beliefs in Constant Sum Games

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  • Pedro Rey-Biel

Abstract

We report experimental results on one-shot two person 3x3 constant sum games played by non-economists without previous experience in the laboratory. Although strategically our games are very similar to previous experiments in which game theory predictions fail dramatically, 80% of actions taken in our ex- periment coincided with the prediction of the unique Nash equilibrium in pure strategies and 73% of actions were best responses to elicited beliefs. We argue how social preferences, presentation effects and belief elicitation procedures may influence how subjects play in simple but non trivial games and explain the diferences we observe with respect to previous work.

Suggested Citation

  • Pedro Rey-Biel, 2007. "Equilibrium Play and Best Response to (Stated) Beliefs in Constant Sum Games," UFAE and IAE Working Papers 676.07, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    • Handle: RePEc:aub:autbar:676.07
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    1. T. Randolph Beard & Richard O. Beil, 1994. "Do People Rely on the Self-Interested Maximization of Others? An Experimental Test," Management Science, INFORMS, vol. 40(2), pages 252-262, February.
    2. Stahl, Dale II & Wilson, Paul W., 1994. "Experimental evidence on players' models of other players," Journal of Economic Behavior & Organization, Elsevier, vol. 25(3), pages 309-327, December.
    3. Kevin A. McCabe & Arijit Mukherji & David E. Runkle, 1994. "An experimental study of learning and limited information in games," Staff Report 176, Federal Reserve Bank of Minneapolis.
    4. Miguel A. Costa-Gomes & Georg Weizsäcker, 2008. "Stated Beliefs and Play in Normal-Form Games," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(3), pages 729-762.
    5. Camerer, Colin & Weigelt, Keith, 1988. "Experimental Tests of a Sequential Equilibrium Reputation Model," Econometrica, Econometric Society, vol. 56(1), pages 1-36, January.
    6. Offerman, Theo & Sonnemans, Joep & Schram, Arthur, 1996. "Value Orientations, Expectations and Voluntary Contributions in Public Goods," Economic Journal, Royal Economic Society, vol. 106(437), pages 817-845, July.
    7. Stahl Dale O. & Wilson Paul W., 1995. "On Players' Models of Other Players: Theory and Experimental Evidence," Games and Economic Behavior, Elsevier, vol. 10(1), pages 218-254, July.
    8. Costa-Gomes, Miguel & Crawford, Vincent P & Broseta, Bruno, 2001. "Cognition and Behavior in Normal-Form Games: An Experimental Study," Econometrica, Econometric Society, vol. 69(5), pages 1193-1235, September.
    9. Huck, Steffen & Weizsacker, Georg, 2002. "Do players correctly estimate what others do? : Evidence of conservatism in beliefs," Journal of Economic Behavior & Organization, Elsevier, vol. 47(1), pages 71-85, January.
    10. Pablo Brañas Garza & Antonio Morales, 2003. "Gender Differences in Prisoners' Dilemma," Economic Working Papers at Centro de Estudios Andaluces E2003/19, Centro de Estudios Andaluces.
    11. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
    12. Mookherjee Dilip & Sopher Barry, 1994. "Learning Behavior in an Experimental Matching Pennies Game," Games and Economic Behavior, Elsevier, vol. 7(1), pages 62-91, July.
    13. Binmore, Ken & Swierzbinski, Joe & Proulx, Chris, 2001. "Does Minimax Work? An Experimental Study," Economic Journal, Royal Economic Society, vol. 111(473), pages 445-464, July.
    14. Reinhard Selten, 1998. "Axiomatic Characterization of the Quadratic Scoring Rule," Experimental Economics, Springer;Economic Science Association, vol. 1(1), pages 43-61, June.
    15. Schotter Andrew & Weigelt Keith & Wilson Charles, 1994. "A Laboratory Investigation of Multiperson Rationality and Presentation Effects," Games and Economic Behavior, Elsevier, vol. 6(3), pages 445-468, May.
    16. Ochs, Jack & Roth, Alvin E, 1989. "An Experimental Study of Sequential Bargaining," American Economic Review, American Economic Association, vol. 79(3), pages 355-384, June.
    17. 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.
    18. Goeree, Jacob K. & Holt, Charles A., 2004. "A model of noisy introspection," Games and Economic Behavior, Elsevier, vol. 46(2), pages 365-382, February.
    19. Ho, Teck-Hua & Camerer, Colin & Weigelt, Keith, 1998. "Iterated Dominance and Iterated Best Response in Experimental "p-Beauty Contests."," American Economic Review, American Economic Association, vol. 88(4), pages 947-969, September.
    20. Mark Walker & John Wooders, 2001. "Minimax Play at Wimbledon," American Economic Review, American Economic Association, vol. 91(5), pages 1521-1538, December.
    21. Ken Binmore, 1998. "Game Theory and the Social Contract - Vol. 2: Just Playing," MIT Press Books, The MIT Press, edition 1, volume 2, number 0262024446, December.
    22. Weizsacker, Georg, 2003. "Ignoring the rationality of others: evidence from experimental normal-form games," Games and Economic Behavior, Elsevier, vol. 44(1), pages 145-171, July.
    23. Johnson, Eric J. & Camerer, Colin & Sen, Sankar & Rymon, Talia, 2002. "Detecting Failures of Backward Induction: Monitoring Information Search in Sequential Bargaining," Journal of Economic Theory, Elsevier, vol. 104(1), pages 16-47, May.
    24. Guth, Werner & Huck, Steffen & Muller, Wieland, 2001. "The Relevance of Equal Splits in Ultimatum Games," Games and Economic Behavior, Elsevier, vol. 37(1), pages 161-169, October.
    25. Yaw Nyarko & Andrew Schotter, 2002. "An Experimental Study of Belief Learning Using Elicited Beliefs," Econometrica, Econometric Society, vol. 70(3), pages 971-1005, May.
    26. Charles A. Holt & Jacob K. Goeree, 1999. "Stochastic Game Theory: For Playing Games, Not Just for Doing Theory," Virginia Economics Online Papers 306, University of Virginia, Department of Economics.
    27. Fey, Mark & McKelvey, Richard D & Palfrey, Thomas R, 1996. "An Experimental Study of Constant-Sum Centipede Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(3), pages 269-287.
    28. Crawford, Vincent P., 2002. "Introduction to Experimental Game Theory," Journal of Economic Theory, Elsevier, vol. 104(1), pages 1-15, May.
    29. Cooper, David J. & Van Huyck, John B., 2003. "Evidence on the equivalence of the strategic and extensive form representation of games," Journal of Economic Theory, Elsevier, vol. 110(2), pages 290-308, June.
    30. Guth, Werner & Schmittberger, Rolf & Schwarze, Bernd, 1982. "An experimental analysis of ultimatum bargaining," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 367-388, December.
    31. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-1326, December.
    32. Mookherjee, Dilip & Sopher, Barry, 1997. "Learning and Decision Costs in Experimental Constant Sum Games," Games and Economic Behavior, Elsevier, vol. 19(1), pages 97-132, April.
    33. McKelvey, Richard D & Page, Talbot, 1990. "Public and Private Information: An Experimental Study of Information Pooling," Econometrica, Econometric Society, vol. 58(6), pages 1321-1339, November.
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    Cited by:

    1. David Danz & Dietmar Fehr & Dorothea Kübler, 2012. "Information and beliefs in a repeated normal-form game," Experimental Economics, Springer;Economic Science Association, vol. 15(4), pages 622-640, December.
    2. Gallice, Andrea, 2007. "Best Responding to What? A Behavioral Approach to One Shot Play in 2x2 Games," Discussion Papers in Economics 1365, University of Munich, Department of Economics.
    3. ATTANASI Giuseppe & NAGEL Rosemarie, 2008. "A Survey of Psychological Games: Theoretical Findings and Experimental Evidence," LERNA Working Papers 08.07.251, LERNA, University of Toulouse.
    4. Gallice, Andrea, 2006. "Predicting one Shot Play in 2x2 Games Using Beliefs Based on Minimax Regret," Economic Theory and Applications Working Papers 12182, Fondazione Eni Enrico Mattei (FEEM).
    5. Spiliopoulos, Leonidas, 2009. "Neural networks as a learning paradigm for general normal form games," MPRA Paper 16765, University Library of Munich, Germany.

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    More about this item

    Keywords

    Experiments; Constant Sum Games; Stated Beliefs;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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