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Single-payoff farsighted stable sets in strategic games with dominant punishment strategies

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  • Toshiyuki Hirai

    (University of Toyama)

Abstract

We investigate farsighted stable sets in a class of strategic games with dominant punishment strategies. In this class of games, each player has a strategy that uniformly minimizes the other players’ payoffs for any given strategies chosen by these other players. We particularly investigate a special class of farsighted stable sets, each of which consists of strategy profiles yielding a single payoff vector. We call such a farsighted stable set as a single-payoff farsighted stable set. We propose a concept called an inclusive set that completely characterizes single-payoff farsighted stable sets in strategic games with dominant punishment strategies. We also show that the set of payoff vectors yielded by single-payoff farsighted stable sets is closely related to the strict $$\alpha $$ α -core in a strategic game. Furthermore, we apply the results to strategic games where each player has two strategies and strategic games associated with some market models.

Suggested Citation

  • Toshiyuki Hirai, 2018. "Single-payoff farsighted stable sets in strategic games with dominant punishment strategies," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(4), pages 1087-1111, November.
    • Handle: RePEc:spr:jogath:v:47:y:2018:i:4:d:10.1007_s00182-017-0597-3
    DOI: 10.1007/s00182-017-0597-3
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    More about this item

    Keywords

    Farsighted stable set; Dominant punishment strategy; Inclusive set; Strict $$alpha $$ α -core;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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