Tullock Brings Perseverance and Suspense to Tug-of-War

We model the dynamic contest between two players as a game of tug-of-war with a Tullock contest success function (CSF). We show that (pure strategy) Markov perfect equilibrium of this game exists, and it is unique. In this equilibrium - in stark contrast to a model of tug-of-war with an all pay auction CSF - players exert positive efforts until the very last battle. Since the outcome of an individual battle is determined stochastically, even disadvantaged players who fell behind will occasionally win battles and hence the advantage likely change hands. We deliver a set of empirically appealing results on effort dynamics.