Contests with a Prize Externality and Stochastic Entry

We analyze a contest with stochastic participation and a prize externality. A unique symmetric equilibrium exists in the contest. We demonstrate that the presence of a prize externality affects individual equilibrium spending but active participants always face the same expected payoff as in a contest without a prize externality. A positive prize externality gives a higher impact on individual equilibrium spending than a negative prize externality. Regardless of the existence and the sign of a prize externality, ex-post over-dissipation occurs if the actual number of participants is sufficiently large. Independent of the prize externality's sign, active participants spend less but face a higher payoff compared to a fixed-participation contest with the same expected number of players.