Asymptotic stability in the Lovász-Shapley replicator dynamic for cooperative games
- 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.
| Document Type: | Article |
|---|---|
| Language: | English |
| Author: | André CasajusORCiD, Michael KrammORCiD, Harald Wiese |
| Chairs and Professorships: | Chair of Economics and Information Systems |
| Center: | Center for Health Care Management and Regulation (CHCMR) |
| DOI: | https://doi.org/10.1016/j.jet.2020.104993 |
| Parent Title (English): | Journal of economic theory |
| ISSN: | 0022-0531 |
| Volume: | 186 |
| Issue: | March 2020 |
| Year of Completion: | 2020 |
| Article Number: | 104993 |
| Tag: | Asymptotic stability; Cooperative game theory; Evolutionary game theory; Lovász-Shapley value; Replicator dynamics; Simple monotonic games |
| Content Focus: | Academic Audience |
| Peer Reviewed: | Yes |
| Rankings: | AJG Ranking / 4 |
| SJR Ranking / Q1 | |
| Licence (German): |  Urheberrechtlich geschützt |