We study a non-cooperative two-sided facility location game in which facilities and clients behave strategically. This is in contrast to many other facility location games in which clients simply visit their closest facility. Facility agents select a location on a graph to open a facility to attract as much purchasing power as possible, while client agents choose which facilities to patronize by strategically distributing their purchasing power in order to minimize their total waiting time. Here, the waiting time of a facility depends on its received total purchasing power. We show that our client stage is an atomic splittable congestion game, which implies existence, uniqueness and efficient computation of a client equilibrium. Therefore, facility agents can efficiently predict client behavior and make strategic decisions accordingly. Despite that, we prove that subgame perfect equilibria do not exist in all instances of this game and that their existence is NP-hard to decide. On the positive side, we provide a simple and efficient algorithm to compute 3-approximate subgame perfect equilibria.

该研究探讨了一个非合作的两侧设施定位博弈，其中设施和客户的行为是战略性的，它呈现出一个原子可分拥堵博弈的客户阶段，从而意味着原始博弈的客户均衡存在、唯一且计算有效。然而，该研究证明了该博弈的所有情况下都不存在子博弈完美均衡，并且存在子博弈完美均衡是NP难的。但积极的一面是，该研究提供了一个简单而有效的算法来计算3-近似的子博弈完美均衡。

最小化总等待时间的客户战略设施位置