Unsolicited prizes in contests

We study two identical contests in which players compete against each other in each contest. A player is awarded a prize if he wins one of the contests, and an additional prize if he wins both contests. We show that in the symmetric equilibrium of either simultaneous or sequential contests, each player’s expected payoff decreases with the value of the additional prize for winning both contests, implying that each player would prefer to be rewarded for winning only one of the contests but never for winning both. We then investigate another variant of two interdependent contests and show that, as in the previous models, additional prizes other than those for a single win may be unsolicited by the players.