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Ex-post regret heuristics under private values (II): 2×2 games

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  • Saran, Rene
  • Serrano, Roberto

Abstract

When information is hardly available, the role of priors should be limited in robust game-theoretic predictions. We analyze a process of heuristics based on ex-post regret as a guide to understand how to play games of incomplete information with private values. While our dynamics has a strong component of inertia, its key is that with a small probability actions are modified in the direction of ex-post regrets. We apply stochastic stability to identify the strategies that will be used in the long run in 2×2 games (i.e., two players with two actions each). For a class of 2×2 games, which includes quasi-supermodular games satisfying “weak dominance”, the resulting theory predicts cautious behavior in the long run, as stochastically stable strategies are minimax regret equilibria. A minimax regret equilibrium is independent of the beliefs about the opponents’ types and actions (only the supports matter) and suggests a “safe way to play the game”.

Suggested Citation

  • Saran, Rene & Serrano, Roberto, 2014. "Ex-post regret heuristics under private values (II): 2×2 games," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 112-123.
  • Handle: RePEc:eee:mateco:v:54:y:2014:i:c:p:112-123
    DOI: 10.1016/j.jmateco.2014.06.004
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    References listed on IDEAS

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    1. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, November.
    2. Beggs Alan, 2009. "Learning in Bayesian Games with Binary Actions," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 9(1), pages 1-30, September.
    3. Saran, Rene & Serrano, Roberto, 2014. "Ex-post regret heuristics under private values (I): Fixed and random matching," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 97-111.
    4. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, November.
    5. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    6. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
    7. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
    8. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
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    Cited by:

    1. Paul Pezanis-Christou & Hang Wu, 2017. "A Naïve Approach to Bidding," School of Economics Working Papers 2017-03, University of Adelaide, School of Economics.
    2. Saran, Rene & Serrano, Roberto, 2014. "Ex-post regret heuristics under private values (I): Fixed and random matching," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 97-111.

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