On the Unique Existence of Pure - Strategy Nash Equilibrium in Smooth Asymmetric Contests

There can be three types of heterogeneity among players in a rent-seeking contest. First, the efectiveness of agent's efort on the winning probabilities may difer among players. Secondly, players may evaluate the rent or prize of the rent-seeking contest diferently. Thirdly, players may face diferent financial constraints. Without assuming that each player’s production function for loteries is diferentiable, Yamazaki (2008) proves under standard assumptions in the literature that there exists a unique pure-strategy Nash equilibrium in a general rent-seeking contest with these three types of heterogeneity among players. In this article, assuming the diferentiability of each player’s production function for loteries, we give a simple proof of Yamazaki’s (2008) result. JEL Classification Numbers: C72, D43, L13.