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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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