A Dynamic Foundation of the Maxmin Criterion

This paper rigorously examines a dynamic foundation of the maxmin criterion (also known as Rawlsian criterion), that selects a social outcome which maximizes the payoff of the worst off agent. In order to understand how the behavior of individual agents shapes up a social preference through repeated long term interactions among agents, we analyze a dynamic matching process in which a long term relationship is embedded. A society is populated with a finite number agents with two different roles, say row and column agents. Two agents are matched, and initiate the long term relationship if both agents agree to do so, which is then subject to a small probability of break-up to dump the agents back to the matching process. We focus on the outcomes sustained by a threshold decision rule slightly perturbed to incorporate sympathy in the spirit of [8]. 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.