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

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Abstract

In contexts in which players have no priors, we analyze a learning pro- cess 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 ran- domly 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 Brown University, Department of Economics in its series Working Papers with number 2010-11.

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Date of creation: 2010
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Handle: RePEc:bro:econwp:2010-11

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Postal: Department of Economics, Brown University, Providence, RI 02912

Related research

Keywords: Fixed and Random Matching; Incomplete Information; Ex-Post Regret Learning; Nash Equilibrium; Ex-Post Equilibrium; Minimax Regret;

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  1. 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.
  2. Sergiu Hart, 2004. "Adaptive Heuristics," Levine's Bibliography 122247000000000471, UCLA Department of Economics.
  3. Dekel, Eddie & Fudenberg, Drew & Levine, David, 2004. "Learning to Play Bayesian Games," Scholarly Articles 3200612, Harvard University Department of Economics.
  4. Rene Saran & Roberto Serrano, 2010. "Regret Matching with Finite Memory," Working Papers 2010-10, Brown University, Department of Economics.
  5. 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.
  6. Ritzberger, Klaus & Weibull, Jorgen W, 1995. "Evolutionary Selection in Normal-Form Games," Econometrica, Econometric Society, vol. 63(6), pages 1371-99, November.
  7. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  8. Spulber, Daniel F, 1995. "Bertrand Competition When Rivals' Costs Are Unknown," Journal of Industrial Economics, Wiley Blackwell, vol. 43(1), pages 1-11, March.
  9. 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).
  10. Hon-Snir, Shlomit & Monderer, Dov & Sela, Aner, 1998. "A Learning Approach to Auctions," Journal of Economic Theory, Elsevier, vol. 82(1), pages 65-88, September.
  11. 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.
  12. 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.
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Cited by:
  1. Rene Saran & Roberto Serrano, 2010. "Regret Matching with Finite Memory," Levine's Working Paper Archive 661465000000000078, David K. Levine.
  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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