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

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  • Rene Saran
  • Roberto Serrano

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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Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 661465000000000083.

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Date of creation: 08 Jun 2010
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Handle: RePEc:cla:levarc:661465000000000083

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  1. Rene Saran & Roberto Serrano, 2010. "Regret Matching with Finite Memory," Levine's Working Paper Archive 661465000000000078, David K. Levine.
  2. 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.
  3. 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.
  4. Dekel, Eddie & Fudenberg, Drew & Levine, David, 2004. "Learning to Play Bayesian Games," Scholarly Articles 3200612, Harvard University Department of Economics.
  5. Ritzberger, Klaus & Weibull, Jorgen W, 1995. "Evolutionary Selection in Normal-Form Games," Econometrica, Econometric Society, Econometric Society, vol. 63(6), pages 1371-99, November.
  6. Rene Saran & Roberto Serrano, 2007. "The Evolution of Bidding Behavior in Private-Values Auction and Double Auctions," Working Papers 2007-01, Brown University, Department of Economics.
  7. Sergiu Hart, 2004. "Adaptive Heuristics," Discussion Paper Series, The Center for the Study of Rationality, Hebrew University, Jerusalem dp372, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  8. Saran Rene & Serrano Roberto, 2010. "Regret Matching with Finite Memory," Research Memorandum 033, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  9. Shlomit Hon-Snir & Dov Monderer & Aner Sela, 1996. "A Learning Approach to Auctions," Game Theory and Information, EconWPA 9610004, EconWPA, revised 07 Oct 1996.
  10. 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.
  11. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, Econometric Society, vol. 61(1), pages 57-84, January.
  12. 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.
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Cited by:
  1. Rene Saran & Roberto Serrano, 2010. "Regret Matching with Finite Memory," Working Papers 2010-10, Brown University, Department of Economics.
  2. Saran Rene & Serrano Roberto, 2010. "Regret Matching with Finite Memory," Research Memorandum 033, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).

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