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

André Casajus, Michael Kramm and Harald Wiese

Journal of Economic Theory, 2020, vol. 186, issue C

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.

Keywords: Cooperative game theory; Evolutionary game theory; Replicator dynamics; Asymptotic stability; Lovász-Shapley value; Simple monotonic games (search for similar items in EconPapers)
JEL-codes: C71 C73 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:jetheo:v:186:y:2020:i:c:s0022053120300028

DOI: 10.1016/j.jet.2020.104993

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