Multiple-Player War of Attrition with Asymmetric Private Values

Abstract

This paper studies a war of attrition over public good provision among multiple ex-ante asymmetric privately informed players. In equilibrium, asymmetry leads to a stratified behavior pattern in which at most one player provides the public good at time zero with a positive probability, while the other players can become active one after another, each at a player-specific activation time, before which even his highest type does not provide the good. The equilibrium is essentially unique: the types who never provide make the players' costs of providing a saddle point of the equilibrium dynamics. Comparing two players in the same war, I show that the one with lower cost, more impatience, or a value distribution tilted toward high values in the sense of a higher revelation rate provides earlier at every value, other things equal. In large societies, the cost of delay is determined by the highest value across players.

arXiv commentJEL Codes: C62; C72; C78; D62; D82; H41 Keywords: war of attrition; public good; asymmetric players; multiple players; incomplete information