On the relationship between Nash—Cournot and Wardrop equilibria

Alain B. Haurie · Patrice Marcotte

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Transportation Planning and Optimization Traffic control and management Game Theory and Applications

Abstract

Abstract A noncooperative game is formulated on a transportation network with congestion. The players are associated with origin‐destination pairs, and are facing demand functions at their respective destination nodes. A Nash‐Cournot equilibrium is defined and conditions for existence and uniqueness of this solution are provided. The asymptotic behavior of the Nash‐Cournot equilibrium is then shown to yield (under appropriate assumptions) a total flow vector corresponding to a Wardrop equilibrium.

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References

1965Existence and Uniqueness of Equilibrium Points for Concave N-Person Games 1971Spatial and temporal price and allocation models 1980Traffic Equilibrium and Variational Inequalities 1979The existence, uniqueness and stability of traffic equilibria 1969Traffic assignment problem for a general network 1984An Efficient Method for Computing Traffic Equilibria in Networks with Asymmetric Transportation Costs

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