Correlated equilibrium implementation: Navigating toward social optima with learning dynamics

Abstract: Implementation theory has made significant advances in characterizing which social choice functions can be implemented in Nash equilibrium, but these results typically assume sophisticated strategic reasoning by agents. However, evidence exists to show that agents frequently cannot perform such reasoning. In this paper, we present a finite mechanism which fully implements Maskin-monotonic social choice functions as the outcome of the unique correlated equilibrium of the induced game. Due to the results in Hart and MasColell (2000), this yields that even when agents use a simple adaptive heuristic like regret minimization rather than computing equilibrium strategies, the designer can expect to implement the SCF correctly. We demonstrate the mechanism's effectiveness through simulations in a bilateral trade environment, where agents using regret matching converge to the desired outcomes despite having no knowledge of others' preferences or the equilibrium structure. The mechanism does not use integer games or modulo games.