A Dynamic Foundation of the Rawlsian Maxmin Criterion

This paper rigorously examines a dynamic foundation of the maxmin criterion (also known as Rawlsian criterion), which selects a social outcome that maximizes the payoff of the worst-off agent. A society is populated with two types of equal and finite numbers of agents, row and column. When two agents, one from each type, are matched, a pair of non-transferable payoffs is drawn from a compact and convex set, and they simultaneously choose whether or not to agree to initiate a long term relationship. They actually form the relationship if they both agree to do so; otherwise, they obtain their respective disagreement payoffs and return to their respective pools of agents, waiting for the next period for a new match. Those who form a long term relationship can unilaterally choose to terminate their relationship in later periods, while if both agree to continue the relationship, they can do so with a high probability less than one. If their relationship is broken, they return to their respective pools as described above. We focus on the outcomes sustained by a threshold decision rule slightly perturbed to incorporate sympathy in the spirit of Hume (1978). For a general class of two person games, as the probability of continuing the long term relationship converges to 1, all agents in the economy almost always play the strongly Pareto efficient Rawlsian outcome, the most egalitarian outcome among strongly Pareto efficient outcomes. The Rawlsian criterion is generated through repeated long term interactions among agents in a decentralized fashion.