Equilibria in Secure Strategies in the Tullock Contest

It is well known that a pure-strategy Nash equilibrium does not exist for a two-player rent-seeking contest when the contest success function parameter is greater than two. We analyze the contest using the concept of equilibrium in secure strategies, which is a generalization of the Nash equilibrium. It is defined by two conditions: (i) no player can make a profitable deviation that decreases the payoff of another player and (ii), for any profitable deviation there is a subsequent deviation by another player, that is profitable for the second deviator and worse than the status quo for the first deviator. We show that such equilibrium always exists in the Tullock contest. Moreover, when the success function parameter is greater than two, this equilibrium is unique up to a permutation of players, and has a lower rent dissipation than in a mixed-strategy Nash equilibrium.