Local market structure in a Hotelling town

Alberto A.  Pinto; João P.  Almeida; Telmo  Parreira

doi:10.3934/jdg.2016004

Article Contents

2016, Volume 3, Issue 1: 75-100. Doi: 10.3934/jdg.2016004

This issue Previous Article Similarity solutions of a multidimensional replicator dynamics integrodifferential equation Next Article Finite composite games: Equilibria and dynamics

Local market structure in a Hotelling town

1.
LIAAD INESC TEC and Department of Mathematics, Faculty of Sciences, University of Porto, Rua do Campo Alegre, 687, 4169-007 Porto
2.
LIAAD-INESC TEC and Polytechnic Institute of Bragança, Campus de Santa Apolónia, 5300-253 Bragança
3.
Department of Mathematics, University of Minho, Campus de Gualtar Braga

Received: September 30, 2015

Revised: December 31, 2015

Published: December 2015

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Abstract

We develop a theoretical framework to study the location-price competition in a Hotelling-type network game, extending the Hotelling model, with linear transportation costs, from a line (city) to a network (town). We show the existence of a pure Nash equilibrium price if, and only if, some explicit conditions on the production costs and on the network structure hold. Furthermore, we prove that the local optimal localization of the firms are at the cross-roads of the town.

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Mathematics Subject Classification: Primary: 91A43, 91A06; Secondary: 91A80, 91A44.

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