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

• 成果类型: Article
• 署名作者: Casajus, Andre; Kramm, Michael; Wiese, Harald
• 署名单位: HHL Leipzig Graduate School of Management; Dortmund University of Technology; Leipzig University
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2020.104993
• 发表日期: 2020
• 关键词: Cooperative game theory; evolutionary game theory; Replicator dynamics; asymptotic stability; Lovasz-Shapley value; Simple monotonic games

摘要

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. (C) 2020 Elsevier Inc. All rights reserved.