Comparative statics of contests and rent-seeking games

This paper develops the comparative statics properties of a contest encountered in patent races and rent-seeking games. I show that symmetric equilibrium expenditure and profit per player decrease with the number of competitors and the discount rate, but increase with the value of the prize. A fundamental lemma established in the paper shows that a stability condition usually imposed on the model is automatically satisfied. I identify a class of likelihood or hazard rate functions for which aggregate expenditure increases with the number of competitors and total profits converge to zero.