A Dynamic Theory for the Class of Games with Nonempty Cores

The core of an n game is defined to be the set of socially stable payoffs, i.e., each payoff is both attainable and no members of a coalition S can gain by leaving the all player coalition and forming S. In this paper we present a dynamic theory for the class of games with nonempty cores which further shows the existence of bargaining schemes that converge to the core, thereby demonstrating that the core is globally stable. The players start with an arbitrary payoff and make a sequence of “corrections” (whenever necessary). It is then shown that any such sequence of payoffs converges to a payoff in the core provided either the coalitions take turns negotiating or maximal corrections are made infinitely often whenever an infinite number of corrections is performed.