Multi-player race

We present a model of race with multiple players and study players' effort choices and expected prizes in equilibrium. We show that, in equilibrium, once any two players win one battle each, the remaining players do not exert any effort anymore. This turns the continuation game into a two-player race. This is different than the results in previous two-player models of race, which report that all states of the game are reached with positive probabilities. We also provide a set of comparative static results on the effects of the number of players and the victory threshold.