Testing the TASP: An Experimental Investigation of Learning in Games with Unstable Equilibria

Abstract

We report experiments designed to test between Nash equilibria that are stable and unstable under learning. The “TASP” (Time Average of the Shapley Polygon) gives a precise prediction about what happens when there is divergence from equilibrium under a wide class of learning processes. We study two versions of Rock-Paper-Scissors with the addition of a fourth strategy, Dumb. The unique Nash equilibrium places a weight of 1/2 on Dumb in both games, but in one game the NE is stable, while in the other game the NE is unstable and the TASP places zero weight on Dumb. Consistent with TASP, we find that the frequency of Dumb is lower and play is further from Nash in the high payoff unstable treatment than in the other treatments. However, the frequency of Dumb is substantially greater than zero in all treatments.games, experiments, TASP, learning, unstable, mixed equilibrium, fictitious play