Contests: A Unique, Mixed Strategy Equilibrium

Abstract

Actions in games that address economic environments such as auctions and oligopoly games are typically costly, and signals, or types, are interdependent. Consequently, such games may not have equilibria supported by monotone strategies, monotone equilibria, see Landsberger and Tsirelson (1999, 2000). Derivation of pure strategy nonmonotone equilibria when types are interdependent and continuously distributed has not been explored in the literature, and it is certainly a non trivial matter; mixed-strategy equilibria pose additional problems. We address these issues by considering a contest game that can be interpreted as competition for research funds or jobs. Assuming a multinormal distribution of signals, we were able to establish a mixed strategy equilibrium and prove that this is the only equilibrium in the class of all equilibria. Various properties of this equilibrium were established. We showed some pitfalls one may encounter by trying to impose a-priori (reasonable) restrictions on strategies, or trying to conduct the analysis assuming a general class of signal distribution.