Caller Number Five and related timing games

Andreas Park and Lones Smith ()
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Lones Smith: Department of Economics, University of Michigan

Theoretical Economics, 2008, vol. 3, issue 2, pages 231-256

Abstract: There are two varieties of timing games in economics: wars of attrition, in which having more predecessors helps, and pre-emption games, in which having more predecessors hurts. This paper introduces and explores a spanning class with rank-order payoffs that subsumes both varieties as special cases. We assume time is continuous, actions are unobserved, and information is complete, and explore how equilibria of the games, in which there is shifting between phases of slow and explosive (positive probability) stopping, capture many economic and social timing phenomena. Inspired by auction theory, we first show how each symmetric Nash equilibrium is equivalent to a different "potential function.'' By using this function, we straightforwardly obtain existence and characterization results. Descartes' Rule of Signs bounds the number of 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 (search for similar items in EconPapers)
JEL-codes: C73 D81 (search for similar items in EconPapers)
Date: 2008 Written 2008-06-01

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Working Paper: Caller Number Five and Related Timing Games (2008)
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