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On the Existence and Computation of Nash Equilibrium in Network Competitive Location Under Delivered Pricing and Price Sensitive Demand

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Abstract

We address the location-price decision problem for firms that offer the same type of product and compete on delivered pricing. If firms set equilibrium prices at demand points, the problem can be seen as a location game for which the Nash equilibrium (NE) is used as solution concept. For spatially separated markets, with inelastic demand, there exists a NE and it can be found by social cost minimization, as happens in network and planar location. However, with price sensitive demand, the existence of a NE has not been proven yet and socially optimal locations may not be a NE. In this paper we show that a NE can be found in discrete and network location when demand is price sensitive. A Mixed Integer Linear Programming formulation is implemented in the best response procedure which allow to find a NE for a variety of demand functions. An empirical study with data of Spanish municipalities is performed in which the procedure is applied to 200 large size test problems with linear, quadratic, exponential and hyperbolic demand functions.

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Data Availability

Data are available on the web site http://www.um.es/geloca/gio/datos-espana-2015.txt.

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Acknowledgements

This research has been supported by the Fundación Séneca (The Agency of Science and Technology of the Region of Murcia) under the research project 19241/PI/14.

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Authors and Affiliations

  1. Dept. Statistics and Operational Research, University of Murcia, 30100 Espinardo, Murcia, Spain

    Blas Pelegrín & Pascual Fernández

  2. Dept. of Business Administration, San Antonio Catholic University, 30107 Guadalupe, Murcia, Spain

    María Dolores García

Authors
  1. Blas Pelegrín
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  2. Pascual Fernández
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  3. María Dolores García
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Correspondence to Blas Pelegrín.

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Appendix

Appendix

Table 3 Results for linear demand function
Full size table
Table 4 Results for quadratic demand function
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Table 5 Results for exponential demand function
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Table 6 Results for hyperbolic demand function
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Pelegrín, B., Fernández, P. & García, M. On the Existence and Computation of Nash Equilibrium in Network Competitive Location Under Delivered Pricing and Price Sensitive Demand. Netw Spat Econ 23, 825–843 (2023). https://doi.org/10.1007/s11067-023-09598-9

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