Multiplayer War of Attrition with Asymmetric Private Information

TL;DR

This paper analyzes a multiplayer war of attrition game with asymmetric private information, revealing how asymmetry influences strategic timing and providing insights into public good provision dynamics.

Contribution

It introduces a model combining multiple players, incomplete information, and asymmetry, deriving a unique equilibrium with stratified behavior patterns.

Findings

Asymmetry causes one player to provide immediately with positive probability.

Players with less patience or lower costs provide faster.

In large societies, delay costs are driven by the highest type of instant-exit players.

Abstract

This paper studies a war of attrition game in the setting of public good provision that combines three elements: (i) multiple players, (ii) incomplete information, and (iii) ex-ante asymmetry. In the unique equilibrium, asymmetry leads to a stratified behavior pattern where one player provides the public good instantly with a positive probability while each of the other players has a player-specific strict waiting time, before which even his highest type will not provide the good. Comparative statics show that a player with less patience, lower cost of provision, and higher reputation in value (expressed in a form of hazard rate) provides the good type-wise uniformly faster. In large societies, the cost of delay is mainly determined by the highest type of the instant-exit player.