# American Institute of Mathematical Sciences

January  2016, 3(1): 75-100. doi: 10.3934/jdg.2016004

## 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, Portugal 2 LIAAD-INESC TEC and Polytechnic Institute of Bragança, Campus de Santa Apolónia, 5300-253 Bragança, Portugal 3 Department of Mathematics, University of Minho, Campus de Gualtar Braga, Portugal

Received  October 2015 Revised  January 2016 Published  March 2016

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.
Citation: Alberto A. Pinto, João P. Almeida, Telmo Parreira. Local market structure in a Hotelling town. Journal of Dynamics & Games, 2016, 3 (1) : 75-100. doi: 10.3934/jdg.2016004
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