This paper studies a class of games, “all-pay contests,” which capture general asymmetries and sunk investments inherent in scenarios such as lobbying, competition for market power, labor-market tournaments, and R&D races. Players compete for one of several identical prizes by choosing a score. Conditional on winning or losing, it is weakly better to do so with a lower score. This formulation allows for differing production technologies, costs of capital, prior investments, attitudes toward risk, and conditional and unconditional investments, among others. I provide a closed-form formula for players' equilibrium payoffs and analyze player participation. A special case of contests is multiprize, complete-information all-pay auctions.
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