In a dynamic matching market, such as a marriage or job market, how should agents balance accepting a proposed match with the cost of continuing their search? We consider this problem in a discrete setting, in which agents have cardinal values and finite lifetimes, and proposed matches are random. We seek to quantify how well the agents can do. We provide upper and lower bounds on the collective losses of the agents, with a polynomially small failure probability, where the notion of loss is with respect to a plausible baseline we define. These bounds are tight up to constant factors. We highlight two aspects of this work. First, in our model, agents have a finite time in which to enjoy their matches, namely the minimum of their remaining lifetime and that of their partner; this implies that unmatched agents become less desirable over time, and suggests that their decision rules should change over time. Second, we use a discrete rather than a continuum model for the population. The discreteness causes variance which induces localized imbalances in the two sides of the market. One of the main technical challenges we face is to bound these imbalances. In addition, we present the results of simulations on moderate-sized problems for both the discrete and continuum versions. For these size problems, there are substantial ongoing fluctuations in the discrete setting whereas the continuum version converges reasonably quickly.

中文翻译：

---

选择匹配：探索与决策

在动态匹配市场（例如婚姻或就业市场）中，代理人应如何平衡接受提议的匹配与继续寻找的成本？我们在离散设置中考虑这个问题，其中代理具有基数和有限的生命周期，并且提议的匹配是随机的。我们试图量化代理的表现。我们提供了代理集体损失的上限和下限，具有多项式小的失败概率，其中损失的概念是关于我们定义的合理基线。这些界限对常数因子非常严格。我们强调这项工作的两个方面。首先，在我们的模型中，代理有有限的时间来享受他们的比赛，即他们剩余的生命周期和他们的合作伙伴的生命周期中的最短时间；这意味着随着时间的推移，不匹配的代理变得越来越不受欢迎，并建议他们的决策规则应该随着时间的推移而改变。其次，我们对总体使用离散模型而不是连续模型。离散性导致差异，从而导致市场两侧的局部不平衡。我们面临的主要技术挑战之一是限制这些不平衡。此外，我们展示了离散和连续版本的中等规模问题的模拟结果。对于这些大小问题，离散设置存在大量持续波动，而连续版本收敛得相当快。我们面临的主要技术挑战之一是限制这些不平衡。此外，我们展示了离散和连续版本的中等规模问题的模拟结果。对于这些大小问题，离散设置中存在大量持续波动，而连续版本收敛得相当快。我们面临的主要技术挑战之一是限制这些不平衡。此外，我们展示了离散和连续版本的中等规模问题的模拟结果。对于这些大小问题，离散设置存在大量持续波动，而连续版本收敛得相当快。