Equilibria in Two-Player Sequential Tullock Contests

This paper provides a fully fledged equilibrium analysis for two-player sequential-move contests with complete information, while allowing for a full spectrum of the contest's accuracy and players' asymmetry. For a strong-lead contest, an interior equilibrium (both players are active) prevails if the contest technology is sufficiently noisy; otherwise, a preemptive equilibrium (the follower is inactive) occurs. For a weak-lead contest, an interior equilibrium always prevails if the leader is sufficiently weak; otherwise, preemptive equilibria occur if and only if the contest's accuracy level is in a middle range. In an interior equilibrium, a nonlinear characteristic equation is identified to pin down the players' effort ratio (and further the effort levels), although there is no analytical solution in general. In a preemptive equilibrium, the leader's effort is the minimum level that shuts down the follower