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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 Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales in its series Working Papers with number 2010-11.

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Date of creation: 08 Jun 2010
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Handle: RePEc:imd:wpaper:wp2010-11

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Keywords: fixed and random matching; incomplete information; ex-post regret learning; nash equilibrium; ex-post equilibrium; minimax regret equilibrium; second-price auction; first-price auction; bertrand duopoly;

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  1. Eddie Dekel & Drew Fudenberg & David K. Levine, 2000. "Learning to Play Bayesian Games," Discussion Papers 1322, Northwestern University, Center for Mathematical Studies in Economics and Management Science, revised Jul 2001.
  2. Hans Jorgen Jacobsen & Mogens Jensen & Birgitte Sloth, 2000. "The Evolution of Conventions under Incomplete Information," Econometric Society World Congress 2000 Contributed Papers 1340, Econometric Society.
  3. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  4. Monderer, Dov & Shlomit Hon-Snir & Aner Sela, 1996. "A Learning Approach to Auctions," Discussion Paper Serie B 388, University of Bonn, Germany.
  5. Sergiu Hart, 2005. "Adaptive Heuristics," Econometrica, Econometric Society, vol. 73(5), pages 1401-1430, 09.
  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. K. Ritzberger & J. Weibull, 2010. "Evolutionary Selection in Normal-Form Games," Levine's Working Paper Archive 452, David K. Levine.
  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. Rene Saran & Roberto Serrano, 2010. "Regret Matching with Finite Memory," Levine's Working Paper Archive 661465000000000078, David K. Levine.
  10. Spulber, Daniel F, 1995. "Bertrand Competition When Rivals' Costs Are Unknown," Journal of Industrial Economics, Wiley Blackwell, vol. 43(1), pages 1-11, March.
  11. 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.
  12. 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.
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Cited by:
  1. Rene Saran & Roberto Serrano, 2010. "Regret matching with finite memory," Working Papers 2010-10, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
  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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