Decentralized dynamics to optimal and stable states in the assignment game

Payoff-driven adjustment dynamics lead to stable and optimal outcomes in decentralized two-sided assignment markets. Pairs of agents from both sides of the market randomly encounter each other and match if `profitable'. Very little information is available, in particular agents have no knowledge of others' preferences, their past actions and payoffs or the value of the different matches. This process implements optimal and stable - i.e. core - allocations even though agents interact asynchronously and randomly, and there is no central authority enforcing matchings or sharing rules.