Wardrop Equilibria with Risk-Averse Users

Transportation Science, Vol. 44, No. 1, pp. 63-86, February 2010

Columbia Business School Research Paper No. 11-27

36 Pages Posted: 20 Oct 2011

See all articles by Nicolas E. Stier-Moses

Nicolas E. Stier-Moses

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Fernando Ordonez

University of Southern California - Epstein Department of Industrial & Systems Engineering

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Date Written: February 1, 2010

Abstract

Network games can be used to model competitive situations in which players select routes to maximize their utility. Common applications include traffic, telecommunication and distribution networks. Although traditional network models have assumed that utilities only depend on congestion, in most applications they also have an uncertain component. In this work, we extend Wardrop's network game (1952) by explicitly incorporating uncertainty in utility functions. Players are utility maximizers and select their route by solving a robust optimization problem, which takes the uncertainty into account. We define a robust Wardrop equilibrium as a solution under which all players are assigned to an optimal solution to their robust problems. Such a solution always exists and can be computed through efficient column generation methods. We show through a computational study that a robust Wardrop equilibrium tends to be more fair than the classic Wardrop equilibrium which ignores the uncertainty. Hence, a robust Wardrop equilibrium is more stable than the nominal counterpart as it reduces the regret that players experience after the uncertainty is revealed. Finally, we show that a pricing mechanism allows the network planner to coordinate players into a socially optimal solution, and show how the necessary tolls can be computed.

Suggested Citation

Stier-Moses, Nicolas E. and Ordonez, Fernando Ivan, Wardrop Equilibria with Risk-Averse Users (February 1, 2010). Transportation Science, Vol. 44, No. 1, pp. 63-86, February 2010 , Columbia Business School Research Paper No. 11-27, Available at SSRN: https://ssrn.com/abstract=1946432

Nicolas E. Stier-Moses (Contact Author)

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Fernando Ivan Ordonez

University of Southern California - Epstein Department of Industrial & Systems Engineering ( email )

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