Structural Equilibrium Characterization in the 'Perpetual Race to Stay Ahead'

I find new results for the `Perpetual Race' analyzed in Horner 2004. The 'Perpetual Race' is an infinite horizon stochastic state space game for which Markov Perfect equilibria are characterized. My results characterize equilibrium strategy structure in a previously unexplored parameter region (spillovers) and offer a new impatience condition for the case examined by Horner (no spillovers). The technique, a generalization of an argument of Horner, uses the fact that a necessary condition for optimality is that an equilibrium strategy is deviation proof with respect to adjacent state pairs