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A note on the existence of Nash equilibrium in the stochastic bottleneck model

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Author Info
Fosgerau, Mogens
Jensen, Henning F.

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Abstract

Consider Vickrey's dynamic bottleneck model of a congested facility. Let capacity be stochastic and assume that identical users minimize expected cost. This note shows that Nash equilibrium does not always exist. A counter-example is provided for the case of linear scheduling costs, where Nash equilibrium does not exist whenever the marginal cost of earliness is sufficiently low. Such a threshold exists for any absolutely continuous distribution of capacity.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 12012.

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Date of creation: 2008
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Handle: RePEc:pra:mprapa:12012

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Related research
Keywords: Bottleneck model; Random capacity; Nash equilibrium;

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Find related papers by JEL classification:
R41 - Urban, Rural, and Regional Economics - - Transportation Systems - - - Transportation: Demand, Supply, and Congestion

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. d'Aspremont, C & Gabszewicz, Jean Jaskold & Thisse, J-F, 1979. "On Hotelling's "Stability in Competition"," Econometrica, Econometric Society, vol. 47(5), pages 1145-50, September. [Downloadable!] (restricted)
  2. DeSerpa, A C, 1971. "A Theory of the Economics of Time," Economic Journal, Royal Economic Society, vol. 81(324), pages 828-46, December. [Downloadable!] (restricted)
  3. Arnott, Richard & de Palma, Andre & Lindsey, Robin, 1999. "Information and time-of-usage decisions in the bottleneck model with stochastic capacity and demand," European Economic Review, Elsevier, vol. 43(3), pages 525-548, March. [Downloadable!] (restricted)
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  4. Richard Arnott & Marvin Kraus, 2003. "Transport Economics," Boston College Working Papers in Economics 553, Boston College Department of Economics. [Downloadable!]
  5. Fosgerau, Mogens, 2008. "Congestion costs in bottleneck equilibrium with stochastic capacity and demand," MPRA Paper 10040, University Library of Munich, Germany. [Downloadable!]
  6. Arnott, Richard & de Palma, Andre & Lindsey, Robin, 1993. "A Structural Model of Peak-Period Congestion: A Traffic Bottleneck with Elastic Demand," American Economic Review, American Economic Association, vol. 83(1), pages 161-79, March. [Downloadable!] (restricted)
  7. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-60, May. [Downloadable!] (restricted)
  8. Richard Arnott & Andre de Palma & Robin Lindsey, 1993. "The Welfare Effects Of Congestion Tolls With Heterogeneous Commuters," Boston College Working Papers in Economics 231, Boston College Department of Economics.
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  1. Fosgerau, Mogens, 2008. "On the relation between the mean and variance of delay in dynamic queues with random capacity and demand," MPRA Paper 11994, University Library of Munich, Germany. [Downloadable!]
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