Equilibrium Selection in Participation Games, with Applications to Security Issuance

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Abstract: In many applied settings, an activity requires a critical mass of participants to be worthwhile. This 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.  We then use this robust framework to study security design in a setting in which issuance revenue is used to fund investments that are, in turn, used to pay distributions on the securities.  We show that all monotone securities are underpriced and that debt is optimal as it is the least underpriced.  Moreover, underpricing in equity offerings can be mitigated by share rationing and a minimum sales requirement.