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Learning in unprofitable games

Author

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  • Gaunersdorfer, Andrea
  • Hofbauer, Josef

Abstract

A game is unprofitable if equilibrium payoffs do not exceed the maximin payoff for each player. In an unprofitable game, Nash equilibrium play has been notoriously difficult to justify. For a class of 3×3 games we analyze whether evolutionary and learning processes lead to Nash play. We find that neither the pure Nash equilibrium nor the pure maximin strategy are stable rest points under the studied dynamics whereas the mixed Nash equilibrium and the quantal response equilibrium may be attractors, repellors or surrounded by periodic orbits.

Suggested Citation

  • Gaunersdorfer, Andrea & Hofbauer, Josef, 2025. "Learning in unprofitable games," Games and Economic Behavior, Elsevier, vol. 151(C), pages 108-126.
    • Handle: RePEc:eee:gamebe:v:151:y:2025:i:c:p:108-126
    DOI: 10.1016/j.geb.2025.03.001
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    Keywords

    Unprofitable games; Nash equilibrium; Maximin strategy; Quantal response equilibrium; Replicator dynamics; Best response dynamics; Logit dynamics;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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