集中动态匹配市场与公用事业的渐近最优控制
Asymptotically Optimal Control of a Centralized Dynamic Matching Market with General Utilities
摘要：
我们考虑一个匹配的市场，买家和卖家到达根据独立的泊松过程在相同的速度和独立放弃市场，如果不匹配后的指数量的时间具有相同的均值。在这个集中的市场中，系统管理者匹配任何买方和卖方的效用是一个一般的随机变量。我们考虑由$n$索引的系统序列，其中$n^{\mathrm{th}}$系统中的到达被加速了一个因子$n$。我们分析了两个家庭的单参数政策：人口阈值政策立即匹配到达代理，只有当在系统中的队友的数量是高于阈值，其最佳可用的队友，和效用阈值政策匹配到达代理，只有当相应的效用高于阈值。使用流体分析的二维马尔可夫过程的买方和卖方，我们表明，当匹配的效用分布是轻尾，人口阈值策略与阈值$\frac{n}{\ln n}$是渐近最优的所有政策，使匹配只在代理到达时期。在重尾的情况下，我们的最佳阈值水平的特点，这两个政策。研究了具有重尾匹配效用的非平衡匹配市场中的效用阈值策略，发现买卖双方具有相同的渐近最优效用阈值。当匹配效用分布是指数分布、均匀分布、帕累托分布和相关帕累托分布时，我们得到最优阈值。我们发现，随着匹配效用分布的右尾变得更重，每个政策的阈值水平（因此市场厚度）增加，效用阈值政策优于人口阈值政策的幅度也增加。
英文摘要：
We consider a matching market where buyers and sellers arrive according to independent Poisson processes at the same rate and independently abandon the market if not matched after an exponential amount of time with the same mean. In this centralized market, the utility for the system manager from matching any buyer and any seller is a general random variable. We consider a sequence of systems indexed by $n$ where the arrivals in the $n^{\mathrm{th}}$ system are sped up by a factor of $n$. We analyze two families of one-parameter policies: the population threshold policy immediately matches an arriving agent to its best available mate only if the number of mates in the system is above a threshold, and the utility threshold policy matches an arriving agent to its best available mate only if the corresponding utility is above a threshold. Using a fluid analysis of the two-dimensional Markov process of buyers and sellers, we show that when the matching utility distribution is light-tailed, the population threshold policy with threshold $\frac{n}{\ln n}$ is asymptotically optimal among all policies that make matches only at agent arrival epochs. In the heavy-tailed case, we characterize the optimal threshold level for both policies. We also study the utility threshold policy in an unbalanced matching market with heavy-tailed matching utilities and find that the buyers and sellers have the same asymptotically optimal utility threshold. We derive optimal thresholds when the matching utility distribution is exponential, uniform, Pareto, and correlated Pareto. We find that as the right tail of the matching utility distribution gets heavier, the threshold level of each policy (and hence market thickness) increases, as does the magnitude by which the utility threshold policy outperforms the population threshold policy.
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