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A Competitive Network Design Problem with Pricing

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  • Phillip J. Lederer

    (University of Rochester, Rochester, New York 14627)

Abstract

This paper presents a simple model of competition between transport firms that captures the interaction of system design, price setting, and consumer choice. Transport competition is modeled as a noncooperative game where firms first select network designs, then prices for transportation between any two nodes. The goal is to find a Nash equilibrium in prices and system designs for all competing firms. Competition is studied under two alternate assumptions about consumer choice: customers can bundle separately purchased legs and customers cannot. If bundling cannot occur, it is shown that unique Nash equilibrium prices exist and that each firm's profit can be written as the difference between two minimum cost flow problems. Sufficient conditions for the existence of equilibrium network designs are also developed. If bundling can occur, it is shown that a price equilibrium may not exist, and if it does, the price equilibrium may not be unique. Lack of existence or uniqueness implies that firm profit is not a well defined function of network designs. This shows that the network design problem with bundling is difficult. With bundling, some results are possible in the case of duopoly competition: an equilibrium in prices always exists but equilibrium prices may not be unique. However, when each firm chooses a network design to maximize the lower bound of its profit, the equilibrium network designs chosen are the same as those chosen when bundling is ignored.

Suggested Citation

  • Phillip J. Lederer, 1993. "A Competitive Network Design Problem with Pricing," Transportation Science, INFORMS, vol. 27(1), pages 25-38, February.
    • Handle: RePEc:inm:ortrsc:v:27:y:1993:i:1:p:25-38
    DOI: 10.1287/trsc.27.1.25
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    Cited by:

    1. Patrice Marcotte & Anne Mercier & Gilles Savard & Vedat Verter, 2009. "Toll Policies for Mitigating Hazardous Materials Transport Risk," Transportation Science, INFORMS, vol. 43(2), pages 228-243, May.
    2. Encaoua, David & Moreaux, Michel & Perrot, Anne, 1996. "Compatibility and competition in airlines demand side network effects," International Journal of Industrial Organization, Elsevier, vol. 14(6), pages 701-726, October.
    3. Richard, Oliver, 2003. "Flight frequency and mergers in airline markets," International Journal of Industrial Organization, Elsevier, vol. 21(6), pages 907-922, June.
    4. Luce Brotcorne & Martine Labbé & Patrice Marcotte & Gilles Savard, 2008. "Joint Design and Pricing on a Network," Operations Research, INFORMS, vol. 56(5), pages 1104-1115, October.
    5. Phillip J. Lederer & Ramakrishnan S. Nambimadom, 1998. "Airline Network Design," Operations Research, INFORMS, vol. 46(6), pages 785-804, December.
    6. Li, Zhi-Chun & Lam, William H.K. & Wong, S.C. & Fu, Xiaowen, 2010. "Optimal route allocation in a liberalizing airline market," Transportation Research Part B: Methodological, Elsevier, vol. 44(7), pages 886-902, August.
    7. Wen, Yuh-Horng & Hsu, Chaug-Ing, 2006. "Interactive multiobjective programming in airline network design for international airline code-share alliance," European Journal of Operational Research, Elsevier, vol. 174(1), pages 404-426, October.
    8. Phillip J. Lederer, 2020. "Location-Price Competition with Delivered Pricing and Elastic Demand," Networks and Spatial Economics, Springer, vol. 20(2), pages 449-477, June.
    9. Youdi Schipper & Piet Rietveld & Peter Nijkamp, 1998. "Deregulation and Schedule Competition in Simple Airline Networks," ERSA conference papers ersa98p205, European Regional Science Association.
    10. Oliver Richard, 2000. "An Empirical Analysis of Marketing Alliances Between Major US Airlines," Econometric Society World Congress 2000 Contributed Papers 1770, Econometric Society.
    11. Xi Wan & Benteng Zou, 2020. "Airport Competition in Two-sided Markets," DEM Discussion Paper Series 20-01, Department of Economics at the University of Luxembourg.
    12. Olivier Armantier & Oliver Richard, 2000. "An Empirical Model of Entry Across Airline Routes with Incomplete Information and Demand Synergies," Econometric Society World Congress 2000 Contributed Papers 1771, Econometric Society.
    13. Adler, Nicole & Smilowitz, Karen, 2007. "Hub-and-spoke network alliances and mergers: Price-location competition in the airline industry," Transportation Research Part B: Methodological, Elsevier, vol. 41(4), pages 394-409, May.

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