Contests with Alternative Public-Good Prizes

I study contests in which a society of players compete, by expending irreversible effort, over which one of alternative prizes should be awarded to them by the decision maker. The prizes are public goods and/or public bads for the players. The players choose their effort levels simultaneously and independently. I define each player's valuation spread as the difference between his valuations for the two public-good/public-bad prizes. I establish that the players' equilibrium effort levels depend solely on their valuation spreads, and that the players never expend positive effort for both prizes in equilibrium. Further, I establish that in equilibrium only players with the widest positive valuation spread and players with the widest negative valuation spread expend positive effort. Finally, I establish that the equilibrium effort level expended for each prize and the equilibrium total effort level are determined only by the widest positive valuation spread and the widest negative valuation spread.