A Perfectly Robust Approach to Multiperiod Matching Problems

Many two-sided matching situations involve multiperiod interaction. Traditional cooperative solutions, such as stability and the core, often identify unintuitive outcomes (or are empty) when applied to such markets. As an alternative, this study proposes the criterion of perfect a stability. An outcome is perfect a-stable if no coalition prefers an alternative assignment in any period that is superior for all plausible market continuations. Behaviorally, the solution combines foresight about the future and a robust evaluation of contemporaneous outcomes. A perfect a-stable matching exists, even when preferences exhibit intertemporal complementarities. A stronger solution, the perfect a-core, is also investigated. Extensions to markets with arrivals and departures, transferable utility, and many-to-one assignments are proposed.