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Asymptotic stability in the Lovász-Shapley replicator dynamic for cooperative games

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  • Casajus, André
  • Kramm, Michael
  • Wiese, Harald

Abstract

We derive population dynamics from finite cooperative games with transferable utility, where the players are interpreted as types of individuals. We show that any asymptotically stable population profile is characterized by a coalition: while the types in the coalition have the same positive share, the other types vanish. The average productivity of such a stable coalition must be greater than the average productivity of any proper sub- or supercoalition. In simple monotonic games, this means that exactly the minimal winning coalitions are stable. Possible applications are the analysis of the organizational structure of businesses or the population constitution of eusocial species.

Suggested Citation

  • Casajus, André & Kramm, Michael & Wiese, Harald, 2020. "Asymptotic stability in the Lovász-Shapley replicator dynamic for cooperative games," Journal of Economic Theory, Elsevier, vol. 186(C).
    • Handle: RePEc:eee:jetheo:v:186:y:2020:i:c:s0022053120300028
    DOI: 10.1016/j.jet.2020.104993
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    More about this item

    Keywords

    Cooperative game theory; Evolutionary game theory; Replicator dynamics; Asymptotic stability; Lovász-Shapley value; Simple monotonic games;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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