Two-player asymmetric contests with ratio-form contest success functions

I examine players' equilibrium effort levels in two-player asymmetric contests with ratio-form contest success functions. I first characterize the Nash equilibrium of the simultaneous-move game. I show that the equilibrium effort ratio is equal to the valuation ratio, and that the prize dissipation ratios for the players are the same. I also show that the prize dissipation ratio for each player is less than or equal to the minimum of the players' probabilities of winning at the Nash equilibrium and thus never exceeds a half Then I examine how the equilibrium effort ratio, the prize dissipation ratios, and the players' equilibrium effort levels respond when the players' valuations for the prize or their abilities change.