Nonlinear Science and Complexity pp 389-395 | Cite as
Uncertainty on a Bertrand Duopoly with Product Differentiation
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Abstract
The conclusions of the Bertrand model of competition are substantially altered by the presence of either differentiated goods or asymmetric information about rival’s production costs. In this paper, we consider a Bertrand competition, with differentiated goods. Furthermore, we suppose that each firm has two different technologies, and uses one of them according to a certain probability distribution. The use of either one or the other technology affects the unitary production cost. We show that this game has exactly one Bayesian Nash equilibrium. We do ex-ante and ex-post analyses of firms’ profits and market prices. We prove that the expected profit of each firm increases with the variance of its production costs. We also show that the expected price of each good increases with both expected production costs, being the effect of the expected production costs of the rival dominated by the effect of the own expected production costs.
Keywords
Game theory Industrial organization Optimization Bertrand model UncertaintyNotes
Acknowledgements
This research was partially supported by the Programs POCTI and POCI by FCT and Ministério da Ciência, Tecnologia e do Ensino Superior. F.A. Ferreira also thanks financial support from ESEIG/IPP and from Centro de Matemática da Universidade do Porto. A.A. Pinto acknowledges financial support from Centro de Matemática da Universidade do Minho.
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