Abstract: 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.
We assume a continuous time setting with unobserved actions and complete information, and explore how equilibria of these games capture many economic and social timing phenomena --- shifting between phases of slow and explosive (positive probability) stopping.
Inspired by auction theory, we first show how the symmetric Nash equilibria are each equivalent to a different "potential function".
This device straightforwardly yields existence and characterization results.
The Descartes Rule of Signs, e.g., bounds the number phase transitions.
We describe how adjacent timing game phases interact:
War of attrition phases are not played out as long as they would be in isolation, but instead are cut short by pre-emptive atoms.
We bound the number of equilibria, and compute the payoff and duration of each equilibrium.
Keywords: Games of Timing, War of Attrition, Preemption Game.
JEL Classification: C73; D81