Stochastic Stability of Group Formation in Collective Action Games

Abstract

We present a game theoretic model of voluntary group formation in collective action and investigate its dynamic stability by applying the stochastic stability theory introduced by Young (1993) and Kandori, Mailath and Rob (1993). The heterogeneity of individuals' preferences yields the multiplicity of strict Nash equilibria including the global defection, the partial cooperation and the full cooperation. Global defection is never stochastically stable when participation costs are small. When the number of individuals with lower motivation to cooperate is larger than a critical level, partial cooperation is uniquely stochastically stable. Otherwise, the stochastic stability selects a version of risk dominant equilibrium. Full cooperation may be stochastically stable if there exists an individual whose incentive to free ride is not so strong. Journal of Economic Literature Classification Numbers: C70, C72.