IDEAS home Printed from https://ideas.repec.org/a/kap/theord/v83y2017i3d10.1007_s11238-017-9595-y.html
   My bibliography  Save this article

Equilibria with vector-valued utilities and preference information. The analysis of a mixed duopoly

Author

Listed:
  • Amparo M. Mármol

    (Universidad de Sevilla)

  • Luisa Monroy

    (Universidad de Sevilla)

  • M. Ángeles Caraballo

    (Universidad de Sevilla)

  • Asunción Zapata

    (Universidad de Sevilla)

Abstract

This paper deals with the equilibria of games when the agents have multiple objectives and, therefore, their utilities cannot be represented by a single value, but by a vector containing the various dimensions of the utility. Our approach allows the incorporation of partial information about the preferences of the agents into the model, and permits the identification of the set of equilibria in accordance with this information. We also propose an additional conservative criterion which can be applied in this framework in order to predict the results of interaction. The potential application of the theoretical results is shown with an analysis of a mixed oligopoly in which the agents value additional objectives other than their own benefit. These objectives are related to social welfare and to the profit of the industry. The flexibility of our approach provides a general theoretical framework for the analysis of a wide range of strategic economic models.

Suggested Citation

  • Amparo M. Mármol & Luisa Monroy & M. Ángeles Caraballo & Asunción Zapata, 2017. "Equilibria with vector-valued utilities and preference information. The analysis of a mixed duopoly," Theory and Decision, Springer, vol. 83(3), pages 365-383, October.
    • Handle: RePEc:kap:theord:v:83:y:2017:i:3:d:10.1007_s11238-017-9595-y
    DOI: 10.1007/s11238-017-9595-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11238-017-9595-y
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11238-017-9595-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Wakker, Peter P, 2001. "Testing and Characterizing Properties of Nonadditive Measures through Violations of the Sure-Thing Principle," Econometrica, Econometric Society, vol. 69(4), pages 1039-1059, July.
    2. Juan Dubra & Fabio Maccheroni & Efe A. Ok, 2004. "Expected Utility Without the Completeness Axiom," Yale School of Management Working Papers ysm404, Yale School of Management.
    3. Shafer, Wayne & Sonnenschein, Hugo, 1975. "Equilibrium in abstract economies without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 345-348, December.
    4. Ok, Efe A., 2002. "Utility Representation of an Incomplete Preference Relation," Journal of Economic Theory, Elsevier, vol. 104(2), pages 429-449, June.
    5. Voorneveld, Mark & Vermeulen, Dries & Borm, Peter, 1999. "Axiomatizations of Pareto Equilibria in Multicriteria Games," Games and Economic Behavior, Elsevier, vol. 28(1), pages 146-154, July.
    6. Dubra, Juan & Maccheroni, Fabio & Ok, Efe A., 2004. "Expected utility theory without the completeness axiom," Journal of Economic Theory, Elsevier, vol. 115(1), pages 118-133, March.
    7. Borm, P.E.M. & Tijs, S.H. & van den Aarssen, J.C.M., 1988. "Pareto equilibria in multiobjective games," Other publications TiSEM a02573c0-8c7e-409d-bc75-0, Tilburg University, School of Economics and Management.
    8. Kozhan, Roman & Salmon, Mark, 2009. "Uncertainty aversion in a heterogeneous agent model of foreign exchange rate formation," Journal of Economic Dynamics and Control, Elsevier, vol. 33(5), pages 1106-1122, May.
    9. Park, Jaeok, 2015. "Potential games with incomplete preferences," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 58-66.
    10. de Fraja, Giovanni & Delbono, Flavio, 1990. "Game Theoretic Models of Mixed Oligopoly," Journal of Economic Surveys, Wiley Blackwell, vol. 4(1), pages 1-17.
    11. William C. Merrill & Norman Schneider, 1966. "Government Firms in Oligopoly Industries: A Short-Run Analysis," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 80(3), pages 400-412.
    12. 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.
    13. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    14. Sagi, Jacob S., 2006. "Anchored preference relations," Journal of Economic Theory, Elsevier, vol. 130(1), pages 283-295, September.
    15. de Fraja, Giovanni & Delbono, Flavio, 1989. "Alternative Strategies of a Public Enterprise in Oligopoly," Oxford Economic Papers, Oxford University Press, vol. 41(2), pages 302-311, April.
    16. ZHAO, Jingang, 1991. "The equilibria of a multiple objective game," LIDAM Reprints CORE 987, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    17. David M. Kreps & Jose A. Scheinkman, 1983. "Quantity Precommitment and Bertrand Competition Yield Cournot Outcomes," Bell Journal of Economics, The RAND Corporation, vol. 14(2), pages 326-337, Autumn.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sasaki, Yasuo, 2022. "Unawareness of decision criteria in multicriteria games," Mathematical Social Sciences, Elsevier, vol. 119(C), pages 31-40.
    2. Anna Rettieva, 2022. "Dynamic Multicriteria Game with Pollution Externalities," Mathematics, MDPI, vol. 10(22), pages 1-15, November.
    3. 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.
    4. Jaeok Park, 2019. "Decision Making and Games with Vector Outcomes," Working papers 2019rwp-146, Yonsei University, Yonsei Economics Research Institute.
    5. Juho Kokkala & Kimmo Berg & Kai Virtanen & Jirka Poropudas, 2019. "Rationalizable strategies in games with incomplete preferences," Theory and Decision, Springer, vol. 86(2), pages 185-204, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Juho Kokkala & Kimmo Berg & Kai Virtanen & Jirka Poropudas, 2019. "Rationalizable strategies in games with incomplete preferences," Theory and Decision, Springer, vol. 86(2), pages 185-204, March.
    3. Bosi, Gianni & Herden, Gerhard, 2012. "Continuous multi-utility representations of preorders," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 212-218.
    4. Jaeok Park, 2019. "Decision Making and Games with Vector Outcomes," Working papers 2019rwp-146, Yonsei University, Yonsei Economics Research Institute.
    5. Evren, Özgür & Ok, Efe A., 2011. "On the multi-utility representation of preference relations," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 554-563.
    6. Gerasímou, Georgios, 2010. "Consumer theory with bounded rational preferences," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 708-714, September.
    7. Susumu Cato, 2013. "Quasi-decisiveness, quasi-ultrafilter, and social quasi-orderings," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(1), pages 169-202, June.
    8. Eric Danan, 2021. "Partial utilitarianism," Working Papers hal-03327900, HAL.
    9. Guo, Liang, 2021. "Contextual deliberation and the choice-valuation preference reversal," Journal of Economic Theory, Elsevier, vol. 195(C).
    10. Simone Cerreia-Vioglio & Alfio Giarlotta & Salvatore Greco & Fabio Maccheroni & Massimo Marinacci, 2020. "Rational preference and rationalizable choice," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(1), pages 61-105, February.
    11. Gorno, Leandro & Rivello, Alessandro T., 2023. "A maximum theorem for incomplete preferences," Journal of Mathematical Economics, Elsevier, vol. 106(C).
    12. Elena Cettolin & Arno Riedl, 2015. "Revealed Incomplete Preferences under Uncertainty," CESifo Working Paper Series 5359, CESifo.
    13. Yasuo Sasaki, 2019. "Rationalizability in multicriteria games," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(2), pages 673-685, June.
    14. Nascimento, Leandro & Riella, Gil, 2011. "A class of incomplete and ambiguity averse preferences," Journal of Economic Theory, Elsevier, vol. 146(2), pages 728-750, March.
    15. Qiyan Ong & Jianying Qiu, 2023. "Paying for randomization and indecisiveness," Journal of Risk and Uncertainty, Springer, vol. 67(1), pages 45-72, August.
    16. Monica Milasi & Domenico Scopelliti, 2021. "A Variational Approach to the Maximization of Preferences Without Numerical Representation," Journal of Optimization Theory and Applications, Springer, vol. 190(3), pages 879-893, September.
    17. Evren, Özgür, 2014. "Scalarization methods and expected multi-utility representations," Journal of Economic Theory, Elsevier, vol. 151(C), pages 30-63.
    18. Simon Grant & Patricia Rich & Jack Stecher, 2021. "Objective and subjective rationality and decisions with the best and worst case in mind," Theory and Decision, Springer, vol. 90(3), pages 309-320, May.
    19. Chambers, Christopher P. & Echenique, Federico, 0. "Empirical welfare economics," Theoretical Economics, Econometric Society.
    20. Giarlotta, Alfio & Greco, Salvatore, 2013. "Necessary and possible preference structures," Journal of Mathematical Economics, Elsevier, vol. 49(2), pages 163-172.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:theord:v:83:y:2017:i:3:d:10.1007_s11238-017-9595-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.