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Finding all pure strategy Nash equilibria in a planar location game

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  • Díaz-Báñez, J.M.
  • Heredia, M.
  • Pelegrín, B.
  • Pérez-Lantero, P.
  • Ventura, I.

Abstract

In this paper, we deal with a planar location-price game where firms first select their locations and then set delivered prices in order to maximize their profits. If firms set the equilibrium prices in the second stage, the game is reduced to a location game for which pure strategy Nash equilibria are studied assuming that the marginal delivered cost is proportional to the distance between the customer and the facility from which it is served. We present characterizations of local and global Nash equilibria. Then an algorithm is shown in order to find all possible Nash equilibrium pairs of locations. The minimization of the social cost leads to a Nash equilibrium. An example shows that there may exist multiple Nash equilibria which are not minimizers of the social cost.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:214:y:2011:i:1:p:91-98
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    2. Blas Pelegrín & Pascual Fernández & María Dolores García, 2023. "On the Existence and Computation of Nash Equilibrium in Network Competitive Location Under Delivered Pricing and Price Sensitive Demand," Networks and Spatial Economics, Springer, vol. 23(4), pages 825-843, December.
    3. Vladimir Marianov & H. A. Eiselt, 2016. "On agglomeration in competitive location models," Annals of Operations Research, Springer, vol. 246(1), pages 31-55, November.
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    5. 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.
    6. Godinho, Pedro & Dias, Joana, 2013. "Two-player simultaneous location game: Preferential rights and overbidding," European Journal of Operational Research, Elsevier, vol. 229(3), pages 663-672.

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