Convergence of reinforcement learning to Nash equilibrium: A search-market experiment

Since the introduction of Reinforcement Learning (RL) in Game Theory, a growing literature is concerned with the theoretical convergence of RL-driven outcomes towards Nash equilibrium. In this paper, we apply this issue to a search-theoretic framework (posted-price market) where sellers are confronted with a population of imperfectly informed buyers and take one decision per period (posted prices) with no direct interactions between sellers. We focus on three different scenarios with varying buyers' characteristics. For each of these scenarios, we quantitatively and qualitatively test whether the learned variable (price strategy) converges to the Nash equilibrium. We also study the impact of the temperature parameter (defining the exploitation/exploration trade off) on these results.