Bidding for a group-specific public-good prize

Abstract

We examine the equilibrium effort levels of individual players and groups in a contest in which two groups compete with each other to win a group-specific public-good prize, the players choose their effort levels simultaneously and independently, and the winning group is determined by the selection rule of all-pay auctions. We first prove nonexistence of a pure-strategy Nash equilibrium, and then construct a mixed-strategy Nash equilibrium. At the Nash equilibrium, the only active player in each group is a player whose valuation for the prize is the highest in that group; all the other players expend zero effort; and the equilibrium effort levels depend solely on two values — the highest valuation for the prize in each group.