Congestion externalities are a well-known phenomenon in transportation and communication networks, healthcare etc. Optimization by self-interested agents in such settings typically results in equilibria which are sub-optimal for social welfare. Pigouvian taxes or tolls, which impose a user charge equal to the negative externality caused by the marginal user to other users, are a mechanism for combating this problem. In this paper, we study a non-atomic congestion game in which heterogeneous agents choose amongst a finite set of heterogeneous servers. The delay at a server is an increasing function of its load. Agents differ in their sensitivity to delay. We show that, while selfish optimisation by agents is sub-optimal for social welfare, imposing admission charges at the servers equal to the Pigouvian tax causes the user equilibrium to maximize social welfare. In addition, we characterize the structure of welfare optimal and of equilibrium allocations.

拥堵外部性是交通和通信网络、医疗保健等领域的众所周知的现象。在这种情况下，自利代理的优化通常会导致社会福利次优的均衡。庇古税或通行费征收的用户费用等于边际用户对其他用户造成的负外部性，是解决这个问题的一种机制。在本文中，我们研究了一个非原子拥塞博弈，其中异构代理在一组有限的异构服务器中进行选择。服务器的延迟是其负载的递增函数。代理对延迟的敏感度不同。我们表明，虽然代理人的自私优化对社会福利来说是次优的，在服务器上征收等于庇古税的入场费会导致用户均衡最大化社会福利。此外，我们描述了福利最优和均衡分配的结构。