Taming selten's horse with impulse response

Abstract

The paper experimentally examines the predictive power of the trembling-hand perfect equilibrium concept in the three-player Game of Selten's Horse. At first sight, our data show little support of the trembling-hand perfect equilibrium and rather favor the imperfect equilibrium. We introduce deterministic impulse response trajectories that converge on the trembling-hand perfect equilibrium. The impulse response trajectories are remarkably close – closer than the trajectories from a reinforcement learning model – to the observed dynamics of the game in the short run (50 periods). The quantal response approach also converges on the trembling-hand perfect equilibrium as the error rates decline, suggesting that the trembling-hand perfect equilibrium may be reached in the long run. In the long run (up to 250 periods), however, behavior seems to settle at a non-equilibrium distribution of strategies that rather supports efficient outcomes, instead of converging to the trembling-hand perfect equilibrium.