Title: Evolutionary game of coalition building 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.