A contest success function for rankings

A contest is a game where several players compete for winning prizes by expending costly efforts. We assume that the outcome of a contest is an ordered partition of the set of players (a ranking) and a contest success function assigns a probability to each possible outcome as a function of players’ efforts. We define a contest success function for contests whose outcome is a ranking of any type, i.e., with any number of players at each rank. This approach is new in contest theory since the axiomatic work has exclusively been on contests with single-winner, whose outcome is a ranking with one player in the first rank and all other players in the second rank. The contest success function is characterized by pair-swap consistency, which is an axiom of independence of irrelevant alternatives and generalizes the main axiom in Skaperdas (1996).