Nested Tullock contests with nonmonotone prizes

This paper demonstrates the possibility of a symmetric “binary-action mixed-strategy equilibrium” in the nested Tullock contest model (Clark and Riis in Public Choice 87:177–184, 1996; Eur J Polit Econ 14(4):605–625, 1998b) with multiple nonmonotone prizes. In this symmetric equilibrium, every player adopts the same mixed strategy: each exerts zero effort with some probability and a constant positive effort otherwise. This new type of equilibrium can coexist with the pure-strategy equilibria established in the literature; it may exist even when those pure-strategy equilibria do not. The coexisting (mixed and pure-strategy) equilibria may induce different levels of effort supply.