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Rationalizable strategies in random games

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  • Pei, Ting
  • Takahashi, Satoru

Abstract

We study point-rationalizable and rationalizable strategies in random games. In a random n×n symmetric game, an explicit formula is derived for the distribution of the number of point-rationalizable strategies, which is of the order n in probability as n→∞. The number of rationalizable strategies depends on the payoff distribution, and is bounded by the number of point-rationalizable strategies (lower bound), and the number of strategies that are not strictly dominated by a pure strategy (upper bound). Both bounds are tight in the sense that there exists a payoff distribution such that the number of rationalizable strategies reaches the bound with a probability close to one. We also show that given a payoff distribution with a finite third moment, as n→∞, all strategies are rationalizable with probability one. Our results qualitatively extend to two-player asymmetric games, but not to games with more than two players.

Suggested Citation

  • Pei, Ting & Takahashi, Satoru, 2019. "Rationalizable strategies in random games," Games and Economic Behavior, Elsevier, vol. 118(C), pages 110-125.
    • Handle: RePEc:eee:gamebe:v:118:y:2019:i:c:p:110-125
    DOI: 10.1016/j.geb.2019.08.011
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