IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v183y2019icp823-841.html
   My bibliography  Save this article

Monotone comparative statics in games with non-monotonic best-replies: Contests and Cournot oligopoly

Author

Listed:
  • Gama, Adriana
  • Rietzke, David

Abstract

In this paper, we employ lattice-theoretic techniques to derive a number of comparative statics in a logit contest – a class of games for which best-replies are generically non-monotonic. Using the same approach, we obtain several comparative statics in a Cournot oligopoly model without imposing the usual assumptions that ensure the game is one of strategic substitutes. Our analysis illustrates how lattice-theoretic techniques can deliver powerful insights in games with non-monotonic best-replies.

Suggested Citation

  • Gama, Adriana & Rietzke, David, 2019. "Monotone comparative statics in games with non-monotonic best-replies: Contests and Cournot oligopoly," Journal of Economic Theory, Elsevier, vol. 183(C), pages 823-841.
  • Handle: RePEc:eee:jetheo:v:183:y:2019:i:c:p:823-841
    DOI: 10.1016/j.jet.2019.08.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022053119300845
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.jet.2019.08.004?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. Richard Cornes & Roger Hartley, 2005. "Asymmetric contests with general technologies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(4), pages 923-946, November.
    2. Konrad, Kai A., 2009. "Strategy and Dynamics in Contests," OUP Catalogue, Oxford University Press, number 9780199549603, November.
    3. William Novshek, 1985. "On the Existence of Cournot Equilibrium," Review of Economic Studies, Oxford University Press, vol. 52(1), pages 85-98.
    4. Rabah Amir & Val E. Lambson, 2000. "On the Effects of Entry in Cournot Markets," Review of Economic Studies, Oxford University Press, vol. 67(2), pages 235-254.
    5. Baye, Michael R & Kovenock, Dan & de Vries, Casper G, 1993. "Rigging the Lobbying Process: An Application of the All-Pay Auction," American Economic Review, American Economic Association, vol. 83(1), pages 289-294, March.
    6. Amegashie, J Atsu, 1999. "The Number of Rent-Seekers and Aggregate Rent-Seeking Expenditures: An Unpleasant Result," Public Choice, Springer, vol. 99(1-2), pages 57-62, April.
    7. Nti, Kofi O, 1997. "Comparative Statics of Contests and Rent-Seeking Games," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(1), pages 43-59, February.
    8. Fang, Hanming, 2002. "Lottery versus All-Pay Auction Models of Lobbying," Public Choice, Springer, vol. 112(3-4), pages 351-371, September.
    9. William Novshek, 1980. "Cournot Equilibrium with Free Entry," Review of Economic Studies, Oxford University Press, vol. 47(3), pages 473-486.
    10. Amir, R., 1996. "Cournot oligopoly and theory of supermodular games," LIDAM Reprints CORE 1228, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. Szidarovszky, Ferenc & Okuguchi, Koji, 1997. "On the Existence and Uniqueness of Pure Nash Equilibrium in Rent-Seeking Games," Games and Economic Behavior, Elsevier, vol. 18(1), pages 135-140, January.
    12. Chowdhury, Subhasish M. & Sheremeta, Roman M., 2011. "Multiple equilibria in Tullock contests," Economics Letters, Elsevier, vol. 112(2), pages 216-219, August.
    13. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    14. Perez-Castrillo, J David & Verdier, Thierry, 1992. "A General Analysis of Rent-Seeking Games," Public Choice, Springer, vol. 73(3), pages 335-350, April.
    15. Amir, Rabah, 1996. "Cournot Oligopoly and the Theory of Supermodular Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 132-148, August.
    16. Alexander Matros, 2006. "Rent-seeking with asymmetric valuations: Addition or deletion of a player," Public Choice, Springer, vol. 129(3), pages 369-380, December.
    17. Seade, Jesus K, 1980. "On the Effects of Entry," Econometrica, Econometric Society, vol. 48(2), pages 479-489, March.
    18. Xavier Vives, 2008. "Innovation And Competitive Pressure," Journal of Industrial Economics, Wiley Blackwell, vol. 56(3), pages 419-469, December.
    19. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
    20. Domenico Menicucci, 2006. "Banning Bidders from All-pay Auctions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(1), pages 89-94, September.
    21. Martin Jensen, 2010. "Aggregative games and best-reply potentials," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 43(1), pages 45-66, April.
    22. Stergios Skaperdas, 1996. "Contest success functions (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 283-290.
    23. Martin Kaae Jensen, 2016. "Existence, Uniqueness, and Comparative Statics in Contests," Springer Series in Game Theory, in: Pierre von Mouche & Federico Quartieri (ed.), Equilibrium Theory for Cournot Oligopolies and Related Games, pages 233-244, Springer.
    24. Acemoglu, Daron & Jensen, Martin Kaae, 2013. "Aggregate comparative statics," Games and Economic Behavior, Elsevier, vol. 81(C), pages 27-49.
    25. Donald M. Topkis, 1978. "Minimizing a Submodular Function on a Lattice," Operations Research, INFORMS, vol. 26(2), pages 305-321, April.
    26. Glenn C. Loury, 1979. "Market Structure and Innovation," The Quarterly Journal of Economics, Oxford University Press, vol. 93(3), pages 395-410.
    27. Dixit, Avinash K, 1987. "Strategic Behavior in Contests," American Economic Review, American Economic Association, vol. 77(5), pages 891-898, December.
    28. Adriana Gama & David Michael Rietzke, 2017. "Robust Comparative Statics in Contests," Working Papers 173174403, Lancaster University Management School, Economics Department.
    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. Kishishita, Daiki & Ozaki, Hiroyuki, 2020. "Public goods game with ambiguous threshold," Economics Letters, Elsevier, vol. 191(C).
    2. Rabah Amir & Igor Evstigneev & Adriana Gama, 2021. "Oligopoly with network effects: firm-specific versus single network," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 1203-1230, April.

    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. Adriana Gama & David Michael Rietzke, 2017. "Robust Comparative Statics in Contests," Working Papers 173174403, Lancaster University Management School, Economics Department.
    2. Acemoglu, Daron & Jensen, Martin Kaae, 2013. "Aggregate comparative statics," Games and Economic Behavior, Elsevier, vol. 81(C), pages 27-49.
    3. Luis Corchón, 2007. "The theory of contests: a survey," Review of Economic Design, Springer;Society for Economic Design, vol. 11(2), pages 69-100, September.
    4. Xu, Jin & Zenou, Yves & Zhou, Junjie, 2019. "Networks in Conflict: A Variational Inequality Approach," CEPR Discussion Papers 13647, C.E.P.R. Discussion Papers.
    5. Andrew J. Monaco & Tarun Sabarwal, 2016. "Games with strategic complements and substitutes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(1), pages 65-91, June.
    6. Fu, Qiang & Wu, Zenan & Zhu, Yuxuan, 2022. "On equilibrium existence in generalized multi-prize nested lottery contests," Journal of Economic Theory, Elsevier, vol. 200(C).
    7. Christian Ewerhart, 2020. "Ordinal potentials in smooth games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(4), pages 1069-1100, November.
    8. Roy, Sunanda & Sabarwal, Tarun, 2012. "Characterizing stability properties in games with strategic substitutes," Games and Economic Behavior, Elsevier, vol. 75(1), pages 337-353.
    9. Sakshi Gupta & Ram Singh, 2018. "On Existence and Properties of Pure-strategy Equilibria under Contests," Working Papers id:12840, eSocialSciences.
    10. Amir, Rabah & De Castro, Luciano, 2017. "Nash equilibrium in games with quasi-monotonic best-responses," Journal of Economic Theory, Elsevier, vol. 172(C), pages 220-246.
    11. Konrad, Kai A., 2007. "Strategy in contests: an introduction [Strategie in Turnieren – eine Einführung]," Discussion Papers, Research Unit: Market Processes and Governance SP II 2007-01, WZB Berlin Social Science Center.
    12. Anne-Christine Barthel & Tarun Sabarwal, 2018. "Directional monotone comparative statics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(3), pages 557-591, October.
    13. Ewerhart, Christian, 2017. "Contests with small noise and the robustness of the all-pay auction," Games and Economic Behavior, Elsevier, vol. 105(C), pages 195-211.
    14. Andrew Monaco & Tarun Sabarwal, 2012. "Monotone Comparative Statics in Games with both Strategic Complements and Strategic Substitutes," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201236, University of Kansas, Department of Economics, revised Aug 2012.
    15. Jia, Hao & Skaperdas, Stergios & Vaidya, Samarth, 2013. "Contest functions: Theoretical foundations and issues in estimation," International Journal of Industrial Organization, Elsevier, vol. 31(3), pages 211-222.
    16. Kyung Hwan Baik & Jong Hwa Lee, 2013. "Endogenous Timing In Contests With Delegation," Economic Inquiry, Western Economic Association International, vol. 51(4), pages 2044-2055, October.
    17. repec:kan:wpaper:201412 is not listed on IDEAS
    18. Magnus Hoffmann & Grégoire Rota‐Graziosi, 2020. "Endogenous timing in the presence of non‐monotonicities," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 53(1), pages 359-402, February.
    19. Rabah Amir, 2005. "Supermodularity and Complementarity in Economics: An Elementary Survey," Southern Economic Journal, John Wiley & Sons, vol. 71(3), pages 636-660, January.
    20. Shuoxun Zhang & Tarun Sabarwal & Li Gan, 2015. "Strategic Or Nonstrategic: The Role Of Financial Benefit In Bankruptcy," Economic Inquiry, Western Economic Association International, vol. 53(2), pages 1004-1018, April.
    21. Amir, Rabah & De Castro, Luciano & Koutsougeras, Leonidas, 2014. "Free entry versus socially optimal entry," Journal of Economic Theory, Elsevier, vol. 154(C), pages 112-125.

    More about this item

    Keywords

    Contests; Supermodularity; Cournot oligopoly; Monotone comparative statics;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

    Statistics

    Access and download statistics

    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:eee:jetheo:v:183:y:2019:i:c:p:823-841. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: http://www.elsevier.com/locate/inca/622869 .

    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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622869 .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.