Caller Number Five : Timing Games

There are two varieties of timing games in economics: Having more predecessors helps in a war of attrition and hurts in a pre-emption game. This paper introduces and explores a spanning class with rank-order payoffs that subsumes both as special cases. Given unobserved actions and complete information, we identify equilibria with a rich enough structure to capture a wide array of economic and social timing phenomena — shifting between phases of slow and explosive entry. Inspired by auction theory, we first show how the symmetric Nash equilibria are each equivalent to a different “potential function”. This device yields rapid existence and characterization results. The Descartes Rule of Signs, eg., bounds the number phase transitions. We describe how adjacent timing game phases interact: Wars of attrition are truncated, and pre-emptive atoms swelled. We bound the number of equilibria, and compute the payoff and duration of each equilibrium. JEL Classification: C73, D81.