Payoff Shares in Two-Player Contests

In contest models with symmetric valuations, equilibrium payoffs are positive shares of the value of the prize. In contrast to a bargaining situation, these shares sum to less than one because a share of the value is lost due to rent-dissipation. We ask: can every such division into payoff shares arise as the outcome of the unique pure-strategy Nash equilibrium of a simple asymmetric contest in which contestants differ in the effectiveness of their efforts? For two-player contests the answer is shown to be positive.