Abstract
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.
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