Evolutionary game of coalition building under external pressure

TL;DR

This paper analyzes a model where small players form coalitions under external pressure, showing that as the number of players grows, the problem simplifies to a deterministic optimization in an infinite-dimensional space.

Contribution

It introduces a limit analysis of the coalition formation model, demonstrating convergence to a deterministic control problem as the number of players increases.

Findings

Convergence of the stochastic model to a deterministic control problem

Behavior characterized in an infinite-dimensional state space

Insights into coalition dynamics under external pressure

Abstract

We study the fragmentation-coagulation (or merging and splitting) evolutionary control model as introduced recently by one of the authors, 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.