# American Institute of Mathematical Sciences

April  2016, 3(2): 121-142. doi: 10.3934/jdg.2016006

## Localization and prices in the quadratic Hotelling model with uncertainty

 1 LIAAD - INESC TEC and Department of Mathematics, Faculty of Science, University of Porto, Rua do Campo Alegre, 687, 4169-007 2 Department of Mathematics and Applications, University of Minho, Campus de Gualtar, 4710-057 Braga, Portugal

Received  October 2015 Revised  February 2016 Published  April 2016

For the quadratic Hotelling model, we study the optimal localization and price strategies under incomplete information on the production costs of the firms. We compute explicitly the pure Bayesian-Nash price duopoly equilibrium and we prove that it does not depend upon the distributions of the production costs of the firms, except on their first moments. We find when the maximal differentiation is a local optimum for the localization strategy of both firms.
Citation: Alberto A. Pinto, Telmo Parreira. Localization and prices in the quadratic Hotelling model with uncertainty. Journal of Dynamics & Games, 2016, 3 (2) : 121-142. doi: 10.3934/jdg.2016006
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