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