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Complete versus Incomplete Information in the Hotelling Model

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Modeling, Dynamics, Optimization and Bioeconomics I

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 73))

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 complete and incomplete information in the production costs of both firms. We compute explicitly the Nash price strategy in the cases of complete and incomplete information. We explicitly determine for the profit, consumer surplus and welfare, the quantitative economical advantages and disadvantages between having complete or incomplete information in the production costs. We prove that, in expected value, the consumer surplus and the welfare are greater with incomplete information than with the complete information and the difference is determined by the variances of the probability distributions. In expected value, the profit it is greater for the firm with higher variance for the probability distribution of its productions costs with incomplete information than with the complete information. However, in expected value, the profit can be smaller for the firm with lower variance for the probability distribution of its productions costs with incomplete information than with the complete information.

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Acknowledgements

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.

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Authors and Affiliations

  1. LIAAD-INESC TEC, Porto, Portugal

    Alberto Adrego Pinto & Telmo Parreira

  2. Faculty of Sciences, Department of Mathematics, University of Porto, Rua do Campo Alegre, 687, 4169-007, Porto, Portugal

    Alberto Adrego Pinto

  3. Department of Mathematics, University of Minho, Campus de Gualtar, 4710-057, Braga, Portugal

    Telmo Parreira

Authors
  1. Alberto Adrego Pinto
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  2. Telmo Parreira
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Correspondence to Alberto Adrego Pinto .

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Editors and Affiliations

  1. University of Porto, Department of Mathematics, Porto, Portugal

    Alberto Adrego Pinto

  2. Univ. of California, Dept. of Agricultural and Resource Economics, Berkeley, California, USA

    David Zilberman

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Pinto, A.A., Parreira, T. (2014). Complete versus Incomplete Information in the Hotelling Model. In: Pinto, A., Zilberman, D. (eds) Modeling, Dynamics, Optimization and Bioeconomics I. Springer Proceedings in Mathematics & Statistics, vol 73. Springer, Cham. https://doi.org/10.1007/978-3-319-04849-9_33

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