Contests with multiple alternative prizes: Public-good/bad prizes and externalities

We study contests in which there are multiple alternative public-good/bad prizes, and the players compete, by expending irreversible effort, over which prize to have awarded to them. Each prize may be a public good for some players and a public bad for the others, and the players expend their effort simultaneously and independently. We first prove the existence of a pure-strategy Nash equilibrium of the game, then establish when the total effort level expended for each prize is unique across the Nash equilibria, and then summarize and highlight other interesting and important properties of the equilibria. Finally, we discuss the effects of heterogeneity of valuations on the players’ equilibrium effort levels and a possible extension of the model.