Multi-Player War of Attrition with Asymmetric Incomplete Information

This paper models a multi-player war of attrition game with asymmetric incomplete information on the private provision of one public good to investigate the effect of ex-ante asymmetry. In the unique equilibrium, asymmetry leads to a stratified behavior pattern such that one player provides the good instantly with a positive probability, while each of the others has no probability of provision before a certain moment which is idiosyncratic. Comparative statics show that one with less patience, lower cost of provision, and higher reputation in valuation provides uniformly faster. The cost of delay is mainly determined by the strongest type, namely the highest type of the instant-exit player. This paper considers two types of introduction of asymmetry: raising the strongest type tends to improve efficiency, whereas controlling the strongest type aligns the effect of asymmetry with the sign of an intuitive measure of the cost of symmetry.