Equilibrium Effort in Games with Homogeneous Production Functions and Homogeneous Valuation

I analyze n-player games in which players exert effort to win part or all of a prize, whose value can either be exogenously given or itself a function of the efforts of an arbitrary subset of contenders. When the functions mapping the vector of efforts into the part of the prize that each player receives in the game and on its value, as well as the cost of effort, exhibit an arbitrary degree of homogeneity, I present a simple way to compute the equilibrium strategy and the sufficient conditions for the existence of a unique interior symmetric pure-strategy Nash equilibrium. The setup nests Malueg and Yates (2006), who exploit homogeneity within the class of rent-seeking contests, and extends it in two directions. In particular, it shows that the properties of homogeneous functions can be used to solve: i) a wider range of rent-seeking contests; ii) other classes of games, like Cournot games with non linear inverse demand and possibly non homogeneous goods.