The equilibrium existence problem in finite network congestion games
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
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This paper discusses the uniqueness of user equilibrium in transportation networks with heterogeneous commuters. Daganzo (1983) proved the uniqueness of (stochastic) user equilibrium when commuters have heterogeneous tastes over possible paths, but identical disutility functions from time costs. We first show, by example, that his result may not apply in general networks if disutility functions are allowed to differ. However, for "simple" transportation networks, we show that user equilibrium is always unique and weakly Pareto efficient (cf. the Braess example) for a general class of utility functions. We investigate whether this result applies to more general networks. We also show that user equilibrium is unique in a dynamic bottleneck model with a simple network. We discuss an interesting relationship between the following two problems: the existence of user equilibrium in a finite model and the uniqueness of user equilibrium in a continuum model. In the appendix, we also provide a proof of a slightly generalized version of Daganzo's theorem.