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

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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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
Contact details of provider: Postal: Department of Economics, Brown University, Providence, RI 02912

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  1. Spulber, Daniel F, 1995. "Bertrand Competition When Rivals' Costs Are Unknown," Journal of Industrial Economics, Wiley Blackwell, vol. 43(1), pages 1-11, March.
  2. 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.
  3. K. Ritzberger & J. Weibull, 2010. "Evolutionary Selection in Normal-Form Games," Levine's Working Paper Archive 452, David K. Levine.
  4. 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.
  5. Sergiu Hart, 2005. "Adaptive Heuristics," Econometrica, Econometric Society, vol. 73(5), pages 1401-1430, 09.
  6. Roberto Serrano & Rene Saran, 2007. "The Evolution Of Bidding Behavior In Private-Values Auctions And Double Auctions," Working Papers wp2007_0712, CEMFI.
  7. 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.
  8. Shlomit Hon-Snir & Dov Monderer & Aner Sela, 1996. "A Learning Approach to Auctions," Game Theory and Information 9610004, EconWPA, revised 07 Oct 1996.
  9. Rene Saran & Roberto Serrano, 2010. "Regret Matching with Finite Memory," Working Papers 2010-10, Brown University, Department of Economics.
  10. 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).
  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. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
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