Equilibrium Selection in Participation Games: A Unified Framework

Abstract
In many applied settings, an activity or project requires a critical mass of participants to be worthwhile. This property can give rise to multiple equilibria. We study seven well-known equilibrium selection theories: two heuristic arguments, two models with rational players, and three from the evolutionary literature. With one exception, each relies on strategic complementarities. We weaken this to a mild single crossing property and show that the theories’ predictions have a common form: an agent plays a best response to some fictional distribution of the participation rate of her opponents.