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

  • Saran Rene
  • Serrano Roberto

    (METEOR)

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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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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  1. Shlomit Hon-Snir & Dov Monderer & Aner Sela, 1996. "A Learning Approach to Auctions," Game Theory and Information 9610004, EconWPA, revised 07 Oct 1996.
  2. Eddie Dekel & Drew Fudenberg & David K. Levine, 2001. "Learning to Play Bayesian Games," Harvard Institute of Economic Research Working Papers 1926, Harvard - Institute of Economic Research.
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  4. Spulber, Daniel F, 1995. "Bertrand Competition When Rivals' Costs Are Unknown," Journal of Industrial Economics, Wiley Blackwell, vol. 43(1), pages 1-11, March.
  5. Rene Saran & Roberto Serrano, 2010. "Regret Matching with Finite Memory," Levine's Working Paper Archive 661465000000000078, David K. Levine.
  6. Rene Saran & Roberto Serrano, 2007. "The evolution of bidding behavior in private-values auctions and double auctions," Working Papers 2007-10, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
  7. Sergiu Hart, 2004. "Adaptive Heuristics," Discussion Paper Series dp372, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  8. Drew Fudenberg & David K. Levine, 1996. "The Theory of Learning in Games," Levine's Working Paper Archive 624, David K. Levine.
  9. Hans Jorgen Jacobsen & Mogens Jensen & Birgitte Sloth, 1997. "The evolution of conventions under incomplete information," Economics Working Papers 475, Department of Economics and Business, Universitat Pompeu Fabra, revised Feb 2000.
  10. Linhart, P. B. & Radner, R., 1989. "Minimax-regret strategies for bargaining over several variables," Journal of Economic Theory, 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, vol. 53(1), pages 83-109, October.
  12. Young, H. Peyton, 2004. "Strategic Learning and its Limits," OUP Catalogue, Oxford University Press, number 9780199269181, December.
  13. Ritzberger, Klaus & Weibull, Jorgen W, 1995. "Evolutionary Selection in Normal-Form Games," Econometrica, Econometric Society, vol. 63(6), pages 1371-99, November.
  14. Sergiu Hart & Andreu Mas-Colell, 2003. "Uncoupled Dynamics Do Not Lead to Nash Equilibrium," American Economic Review, American Economic Association, vol. 93(5), pages 1830-1836, December.
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