Price competition in the Hotelling model with uncertainty on costs

Abstract

For the linear Hotelling model with firms located at the boundaries of the segment line, we study the price competition in a scenario of incomplete information in the production costs of both firms. We introduce the bounded uncertain costs (BUC) condition in the production costs and we prove that there is a local optimum price strategy if and only if the BUC condition holds. We compute explicitly the local optimum price strategy and we prove that it does not depend upon the distributions of the production costs of the firms, except on their first moments. We prove that the ex-post profit of a firm is smaller than its ex-ante profit if and only if the production cost of the other firm is greater than its expected cost.

Keywords:

• Hotelling model
• price competition
• duopoly
• uncertainty

AMS Subject Classifications:

• 91B24
• 91B38
• 91B44

Acknowledgments

We are thankful to the anonymous referees for their suggestions. We acknowledge the financial support of LIAAD-INESC TEC through Strategic Project-LA 14-2013–2014 with reference PEst-C/EEI/LA0014/2013, USP-UP project, IJUP, Faculty of Sciences, University of Porto, Calouste Gulbenkian Foundation, FEDER, POCI 2010 and COMPETE Programmes and Fundação para a Ciência e a Tecnologia (FCT) through Project Dynamics and Applications, with reference PTDC/MAT/121107/2010. Telmo Parreira thanks FCT for the PhD scholarship SFRH/BD/33762/2009.