Equilibrium Effort in Games with Homogeneous Production Functions and Homogeneous Valuation

I focus on symmetric n-player games in which players exert effort to win part or all of a prize, whose value can either be exogenously given or endogenously determined. Under homogeneity assumptions on the functions mapping the vector of efforts into the part of the prize that each player receives and on the value of the prize, I derive an explicit solution for pure-strategy symmetric equilibria and show that such assumptions are sufficient to substantially simplify the derivation of the best response functions. I solve for equilibria in situations in which, not only relative efforts matter (homogeneity of degree zero), but efforts increase global production, the shares of global production and their value. The setup nests Malueg and Yates (2006), who study the implications of homogeneous contest success functions of degree zero in rent-seeking games.