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Nash equilibria in location games on a network

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  • Mercedes Pelegrín

    (University of Murcia)

  • Blas Pelegrín

    (University of Murcia)

Abstract

We study the existence and determination of Nash equilibria (NE) in location games where firms compete for the market with the aim of profit maximization. Each competing firm locates one facility at one point on a network and customers, which are located at the nodes of the network, distribute their buying power between the firms from which they get a minimum price. Two cases are considered depending on price policy: mill pricing and delivered pricing. In the former, the existence of NE depends on the structure of the network and the distribution of demand among its nodes. We give some conditions for the existence of NE, taking into account whether co-location is permitted and whether locations are restricted to nodes. Regarding delivered pricing policy, NE always exist at the nodes if production cost along any edge of the network is concave. A mixed integer linear programming formulation is proposed to find them.

Suggested Citation

  • Mercedes Pelegrín & Blas Pelegrín, 2017. "Nash equilibria in location games on a network," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(3), pages 775-791, July.
    • Handle: RePEc:spr:orspec:v:39:y:2017:i:3:d:10.1007_s00291-017-0472-4
    DOI: 10.1007/s00291-017-0472-4
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    References listed on IDEAS

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    1. de Palma, Andre & Ginsburgh, Victor & Thisse, Jacques-Francois, 1987. "On Existence of Location Equilibria in the 3-Firm Hotelling Problem," Journal of Industrial Economics, Wiley Blackwell, vol. 36(2), pages 245-252, December.
    2. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
    3. LEDERER, Philip J. & THISSE, Jacques-François, 1990. "Competitive location on networks under delivered pricing," LIDAM Reprints CORE 893, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Martine Labbé & S. Louis Hakimi, 1991. "Market and Locational Equilibrium for Two Competitors," Operations Research, INFORMS, vol. 39(5), pages 749-756, October.
    5. Blas Pelegrín & Rafael Suárez-Vega & Saúl Cano, 2012. "Isodistant points in competitive network facility location," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 639-660, October.
    6. ReVelle, C. S. & Eiselt, H. A., 2005. "Location analysis: A synthesis and survey," European Journal of Operational Research, Elsevier, vol. 165(1), pages 1-19, August.
    7. Díaz-Báñez, J.M. & Heredia, M. & Pelegrín, B. & Pérez-Lantero, P. & Ventura, I., 2011. "Finding all pure strategy Nash equilibria in a planar location game," European Journal of Operational Research, Elsevier, vol. 214(1), pages 91-98, October.
    8. Plastria, Frank, 2001. "Static competitive facility location: An overview of optimisation approaches," European Journal of Operational Research, Elsevier, vol. 129(3), pages 461-470, March.
    9. d'Aspremont, C & Gabszewicz, Jean Jaskold & Thisse, J-F, 1979. "On Hotelling's "Stability in Competition"," Econometrica, Econometric Society, vol. 47(5), pages 1145-1150, September.
    10. H. A. Eiselt & Gilbert Laporte, 1993. "The Existence of Equilibria in the 3-Facility Hotelling Model in a Tree," Transportation Science, INFORMS, vol. 27(1), pages 39-43, February.
    11. Farahani, Reza Zanjirani & Rezapour, Shabnam & Drezner, Tammy & Fallah, Samira, 2014. "Competitive supply chain network design: An overview of classifications, models, solution techniques and applications," Omega, Elsevier, vol. 45(C), pages 92-118.
    12. A. J. Goldman, 1971. "Optimal Center Location in Simple Networks," Transportation Science, INFORMS, vol. 5(2), pages 212-221, May.
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