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Ex-Post Regret Learning in Games with Fixed and Random Matching: The Case of Private Values

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  • Saran Rene
  • Serrano Roberto

    (METEOR)

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    Abstract

    In contexts in which players have no priors, we analyze a learning process based on ex-post regret as a guide to understand how to play games of incomplete information under private values. The conclusions depend on whether players interact within a fixed set (fixed matching) or they are randomly matched to play the game (random matching). The relevant long run predictions are minimal sets that are closed under “the same or better reply”operations. Under additional assumptions in each case, the prediction boils down to pure Nash equilibria, pure ex-post equilibria or pure minimax regret equilibria. These three paradigms exhibit nice robustness properties in the sense that they are independent of beliefs about the exogenous uncertainty of type spaces. The results are illustrated in second-price auctions, first-price auctions and Bertrand duopolies.

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    Bibliographic Info

    Paper provided by Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR) in its series Research Memorandum with number 032.

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    Date of creation: 2010
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    Handle: RePEc:unm:umamet:2010032

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    Keywords: microeconomics ;

    References

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    1. Sergiu Hart, 2004. "Adaptive Heuristics," Levine's Bibliography 122247000000000471, UCLA Department of Economics.
    2. Hon-Snir, Shlomit & Monderer, Dov & Sela, Aner, 1998. "A Learning Approach to Auctions," Journal of Economic Theory, Elsevier, Elsevier, vol. 82(1), pages 65-88, September.
    3. Eddie Dekel & Drew Fudenberg & David K. Levine, 2001. "Learning to Play Bayesian Games," Harvard Institute of Economic Research Working Papers, Harvard - Institute of Economic Research 1926, Harvard - Institute of Economic Research.
    4. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, The MIT Press, edition 1, volume 1, number 0262061945, December.
    5. Rene Saran & Roberto Serrano, 2007. "The evolution of bidding behavior in private-values auctions and double auctions," Working Papers, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales 2007-10, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
    6. Mogens Jensen & Birgitte Sloth & Hans Jørgen Whitta-Jacobsen, . "The Evolution of Conventions under Incomplete Information," Discussion Papers 03-12, University of Copenhagen. Department of Economics, revised Mar 2003.
    7. Ritzberger, Klaus & Weibull, Jörgen W., 1993. "Evolutionary Selection in Normal Form Games," Working Paper Series, Research Institute of Industrial Economics 383, Research Institute of Industrial Economics.
    8. Rene Saran & Roberto Serrano, 2010. "Regret Matching with Finite Memory," Levine's Working Paper Archive 661465000000000078, David K. Levine.
    9. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, Econometric Society, vol. 61(1), pages 57-84, January.
    10. Linhart, P. B. & Radner, R., 1989. "Minimax-regret strategies for bargaining over several variables," Journal of Economic Theory, Elsevier, Elsevier, vol. 48(1), pages 152-178, June.
    11. Ely, Jeffrey C. & Sandholm, William H., 2005. "Evolution in Bayesian games I: Theory," Games and Economic Behavior, Elsevier, Elsevier, vol. 53(1), pages 83-109, October.
    12. Young, H. Peyton, 2004. "Strategic Learning and its Limits," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780199269181, October.
    13. Spulber, Daniel F, 1995. "Bertrand Competition When Rivals' Costs Are Unknown," Journal of Industrial Economics, Wiley Blackwell, Wiley Blackwell, vol. 43(1), pages 1-11, March.
    14. Sergiu Hart & Andreu Mas-Colell, 2003. "Uncoupled Dynamics Do Not Lead to Nash Equilibrium," American Economic Review, American Economic Association, American Economic Association, vol. 93(5), pages 1830-1836, December.
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    Cited by:
    1. Rene Saran & Roberto Serrano, 2012. "Regret Matching with Finite Memory," Dynamic Games and Applications, Springer, Springer, vol. 2(1), pages 160-175, March.
    2. Fernando Louge & Frank Riedel, 2010. "Evolutionary Stability of First Price Auctions," Working Papers, Bielefeld University, Center for Mathematical Economics 435, Bielefeld University, Center for Mathematical Economics.
    3. Rene Saran & Roberto Serrano, 2010. "Regret Matching with Finite Memory," Levine's Working Paper Archive 661465000000000078, David K. Levine.

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