A two-sided market consists of two sets of agents, each of whom have preferences over the other (Airbnb, Upwork, Lyft, Uber, etc.). We propose and analyze a repeated matching problem, where some set of matches occur on each time step, and our goal is to ensure fairness with respect to the cumulative allocations over an infinite time horizon. Our main result is a polynomial-time algorithm for additive, symmetric (v_i(j) = v_j(i)), and binary (v_i(j) \in \{a,1\}) valuations that both (1) guarantees "envy-freeness up to a single match" (EF1) and (2) selects a maximum weight matching on each time step. Thus for this class of valuations, fairness can be achieved without sacrificing economic efficiency. This result holds even for "dynamic valuations", i.e., valuations that change over time. Although symmetry is a strong assumption, we show that this result cannot be extended to asymmetric binary valuations: (1) and (2) together are impossible even when valuations do not change over time, and for dynamic valuations, even (1) alone is impossible. To our knowledge, this is the first analysis of envy-freeness in a repeated matching setting.

中文翻译：

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双边市场中几乎无嫉妒的重复匹配

双边市场由两组代理组成，每个代理都比另一组有偏好（Airbnb、Upwork、Lyft、Uber 等）。我们提出并分析了一个重复匹配问题，其中每个时间步都会发生一些匹配，我们的目标是确保在无限时间范围内累积分配的公平性。我们的主要结果是用于加法、对称 (v_i(j) = v_j(i)) 和二进制 (v_i(j) \in \{a,1\}) 估值的多项式时间算法，这两个 (1) 都保证“ envy-freeness up to a single match”（EF1）和（2）在每个时间步选择最大权重匹配。因此，对于此类估值，可以在不牺牲经济效益的情况下实现公平。这一结果甚至适用于“动态估值”，即随时间变化的估值。虽然对称性是一个强有力的假设，我们表明，这个结果不能扩展到非对称二元估值：即使估值不随时间变化，（1）和（2）一起也是不可能的，对于动态估值，即使（1）单独也是不可能的。据我们所知，这是对重复匹配设置中无嫉妒的首次分析。