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Cournot competition under uncertainty: conservative and optimistic equilibria

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  • M. Caraballo
  • A. Mármol
  • L. Monroy
  • E. Buitrago

Abstract

In this paper we analyze competition between firms with uncertain demand functions. A duopoly model is considered in which two identical firms producing homogeneous commodities compete in quantities. They face uncertain market demand in a context in which two different future scenarios are possible, and no information about the probability distribution of occurrence of the scenarios is available. This decision-making situation is formalized as a normal-form game with vector-valued utility functions for which the notion of Pareto equilibrium is adopted as a natural extension of that of Cournot equilibrium. Under standard assumptions about the demand functions, we characterize the complete set of Pareto equilibria. In the second part of the paper, we analyse the equilibria to which the agents will arrive depending on their attitude to risk. We find that equilibria always exist if both agents are simultaneously pessimistic or optimistic. In the non-trivial cases, for pessimistic firms, infinitely many equilibria exist, whereas when firms act optimistically, only those pairs of strategies corresponding to the Cournot equilibria in each scenario can be equilibria. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • M. Caraballo & A. Mármol & L. Monroy & E. Buitrago, 2015. "Cournot competition under uncertainty: conservative and optimistic equilibria," Review of Economic Design, Springer;Society for Economic Design, vol. 19(2), pages 145-165, June.
    • Handle: RePEc:spr:reecde:v:19:y:2015:i:2:p:145-165
    DOI: 10.1007/s10058-015-0171-z
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    References listed on IDEAS

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    1. Asplund, Marcus, 2002. "Risk-averse firms in oligopoly," International Journal of Industrial Organization, Elsevier, vol. 20(7), pages 995-1012, September.
    2. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    3. Vives, Xavier, 1984. "Duopoly information equilibrium: Cournot and bertrand," Journal of Economic Theory, Elsevier, vol. 34(1), pages 71-94, October.
    4. Sophie Bade, 2005. "Nash equilibrium in games with incomplete preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(2), pages 309-332, August.
    5. Fulvio Fontini, 2005. "Cournot Oligopoly Under Strategic Uncertainty With Optimistic And Pessimistic Firms," Metroeconomica, Wiley Blackwell, vol. 56(3), pages 318-333, July.
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    Citations

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    Cited by:

    1. A. Zapata & M. A. Caraballo & L. Monroy & A. M. Mármol, 2019. "Hurwicz’s criterion and the equilibria of duopoly models," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(4), pages 937-952, December.
    2. D. V. Borrero & M. A. Hinojosa & A. M. Mármol, 2016. "Stable solutions for multiple scenario cost allocation games with partial information," Annals of Operations Research, Springer, vol. 245(1), pages 209-226, October.
    3. Haiyang Xia, 2021. "Price and quantity competition in a differentiated duopoly with heterogeneous beliefs," Manchester School, University of Manchester, vol. 89(1), pages 46-69, January.
    4. A. Zapata & A. M. Mármol & L. Monroy & M. A. Caraballo, 2019. "A Maxmin Approach for the Equilibria of Vector-Valued Games," Group Decision and Negotiation, Springer, vol. 28(2), pages 415-432, April.
    5. Anna Rettieva, 2022. "Dynamic Multicriteria Game with Pollution Externalities," Mathematics, MDPI, vol. 10(22), pages 1-15, November.
    6. Georgios Gerasimou, 2019. "Dominance-solvable multicriteria games with incomplete preferences," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 165-171, December.

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    More about this item

    Keywords

    Pareto equilibria; Cournot games; Uncertainty; Attitude to risk; D43; D81; L10;
    All these keywords.

    JEL classification:

    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • L10 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - General

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