On the local stability of Nash equilibria in the model of endogenous coalition formation

We study a model of endogenous coalition formation by players (agents) from large societies. Each agent’s preferences are described by his ideal point, while the agents are distributed on the ideal points set according to some rule. The coalition policy is determined as a median of its members ideal points distribution. The payoff of an agent depends on the distance between his ideal point and the policy of the coalition he joins and on the size of this coalition. We assume that the agents distribution has a quasi-concave density function. We find sufficient and necessary conditions for the Nash equilibria to be stable in regard to local unification.