Evolutionary game of coalition building under external pressure

Alekos Cecchin, Vassili N. Kolokoltsov

Research output

Abstract

We study the fragmentation-coagulation, or merging and splitting, model as introduced in Kolokoltsov (Math Oper Res, 2016, in press, doi:10.1287/moor.2016.0838), where N small players can form coalitions to resist to the pressure exerted by the principal. It is a Markov chain in continuous time, and the players have a common reward to optimize. We study the behavior as N grows and show that the problem converges to a (one player) deterministic optimization problem in continuous time, in the infinite dimensional state space l1. We apply the method developed in Gast et al. (IEEE Trans Autom Control 57:2266–2280, 2012), adapting it to our different framework. We use tools involving dynamics in l1, generators of Markov processes, martingale problems, and coupling of Markov chains.

Original languageEnglish
Title of host publicationAnnals of the International Society of Dynamic Games
PublisherBirkhäuser Verlag AG
Pages71-106
Number of pages36
DOIs
Publication statusPublished - 1 Jan 2017

Publication series

NameAnnals of the International Society of Dynamic Games
Volume15
ISSN (Print)2474-0179
ISSN (Electronic)2474-0187

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Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

Cite this

Cecchin, A., & Kolokoltsov, V. N. (2017). Evolutionary game of coalition building under external pressure. In Annals of the International Society of Dynamic Games (pp. 71-106). (Annals of the International Society of Dynamic Games; Vol. 15). Birkhäuser Verlag AG. https://doi.org/10.1007/978-3-319-70619-1_4