A Mechanism for Optimal Enforcement of Coordination: Sidestepping Theory of Mind

Mechanisms employing fines and rewards may be introduced in multi-equilibrium situations to enforce a certain equilibrium. The mechanism does two things. First, it produces a signal disrupting the normal dynamics of repeated play; potentially encouraging agents to reconsider their expectations. Secondly, it changes the payoffs. In deciding what behavior to engage in after introduction of a new mechanism a rational agent needs to consider to what degree the signal has been received and convinced others, which in turn depends on what those others believe about the reception of the signal, and so on. The epistemic mess is a challenge for both the agents and for a policy maker interested in facilitating a re-coordination. The latter begs the question: How large must fines and rewards be to ensure re-coordination? We show that the result we get from classic game theory is more "heavy handed" than necessary; far less intervention is actually required. Specifically we will outline a mechanism that ensures re-coordination, regardless of the idiosyncratic belief formation processes of the population, while at the same time making minimal interventions.