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

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  • 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
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    1. William Novshek, 1985. "On the Existence of Cournot Equilibrium," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(1), pages 85-98.
    2. Rabah Amir & Val E. Lambson, 2000. "On the Effects of Entry in Cournot Markets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(2), pages 235-254.
    3. J. David Pérez-Castrillo & Thierry Verdier, 1992. "A general analysis of rent-seeking games," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 133-148, Springer.
    4. 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.
    5. 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.
    6. Stergios Skaperdas, 1996. "Contest success functions (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 283-290.
    7. Chowdhury, Subhasish M. & Sheremeta, Roman M., 2011. "Multiple equilibria in Tullock contests," Economics Letters, Elsevier, vol. 112(2), pages 216-219, August.
    8. Acemoglu, Daron & Jensen, Martin Kaae, 2013. "Aggregate comparative statics," Games and Economic Behavior, Elsevier, vol. 81(C), pages 27-49.
    9. Glenn C. Loury, 1979. "Market Structure and Innovation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 93(3), pages 395-410.
    10. 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.
    11. William Novshek, 1980. "Cournot Equilibrium with Free Entry," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(3), pages 473-486.
    12. 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).
    13. Amir, Rabah, 1996. "Cournot Oligopoly and the Theory of Supermodular Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 132-148, August.
    14. 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.
    15. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    16. Dixit, Avinash K, 1987. "Strategic Behavior in Contests," American Economic Review, American Economic Association, vol. 77(5), pages 891-898, December.
    17. Adriana Gama & David Michael Rietzke, 2017. "Robust Comparative Statics in Contests," Working Papers 173174403, Lancaster University Management School, Economics Department.
    18. Xavier Vives, 2008. "Innovation And Competitive Pressure," Journal of Industrial Economics, Wiley Blackwell, vol. 56(3), pages 419-469, December.
    19. Konrad, Kai A., 2009. "Strategy and Dynamics in Contests," OUP Catalogue, Oxford University Press, number 9780199549603.
    20. 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.
    21. 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.
    22. Fang, Hanming, 2002. "Lottery versus All-Pay Auction Models of Lobbying," Public Choice, Springer, vol. 112(3-4), pages 351-371, September.
    23. Seade, Jesus K, 1980. "On the Effects of Entry," Econometrica, Econometric Society, vol. 48(2), pages 479-489, March.
    24. 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.
    25. 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.
    26. Alexander Matros, 2006. "Rent-seeking with asymmetric valuations: Addition or deletion of a player," Public Choice, Springer, vol. 129(3), pages 369-380, December.
    27. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
    28. Donald M. Topkis, 1978. "Minimizing a Submodular Function on a Lattice," Operations Research, INFORMS, vol. 26(2), pages 305-321, April.
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    Cited by:

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    2. Kishishita, Daiki & Ozaki, Hiroyuki, 2020. "Public goods game with ambiguous threshold," Economics Letters, Elsevier, vol. 191(C).
    3. 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.

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    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

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