Multi-item contests

Contests are games in which the players compete for a valuable prize by exerting effort or using resources so as to increase their probability of winning. This paper examines two player multi-item contests, a class of games in which players are faced with a decision about how much of a given resource to devote to an entire collection or sequence of different contests. Applications include multi-item rent-seeking behavior, multi-good marketing and advertising, multi-jurisdictional political contests. In these games, even when the (uncertain) outcomes in each contest are assumed to be mutually statistically independent, equilibrium efforts can exhibit strong interdependencies. Changes in either the contest success function or value of the prize in one contest usually alter the equilibrium amount of resources devoted to all contests by both players. We unify and extend results from marketing and political science, and also derive conditions under which both players exert zero effort in equilibrium in some subset of contests.