Equilibrium effort in games with homogeneous production functions and homogeneous valuation

In this study, I analyze games in which the functions mapping a vector of efforts into each player's share of the prize and its value exhibit an arbitrary degree of homogeneity. I present a simple way to compute the equilibrium strategy and sufficient conditions for a unique interior symmetric pure-strategy Nash equilibrium. The setup nests Malueg and Yates (2006), who exploit homogeneity for rent-seeking contests with exogenous prize valuation, and shows that homogeneity can be used to solve (i) a wider range of rent-seeking contests and (ii) other classes of games, like Cournot games with nonlinear inverse demand and possibly non homogeneous goods.