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Existence, Uniqueness, and Comparative Statics in Contests

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  • Martin Kaae Jensen

Abstract

Many important games are aggregative allowing for robust comparative statics analysis even when a game does not exhibit strategic complements or substitutes (Acemoglu and Jensen (2013)). This paper establishes such comparative statics results for contests improving upon existing results by (i) allowing payoff functions to be discontinuous at the origin, and (ii) allowing for asymmetric rent-seeking contests and patent races. A leading example where (i) is relevant is the classical Tullock contest (Tullock (1980)). The paper also studies existence and uniqueness of equilibria extending the results of Szidarovszky and Okuguchi (1997) and Cornes and Hartley (2005) to patent races.

Suggested Citation

  • Martin Kaae Jensen, 2015. "Existence, Uniqueness, and Comparative Statics in Contests," Discussion Papers in Economics 15/16, Division of Economics, School of Business, University of Leicester.
    • Handle: RePEc:lec:leecon:15/16
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Kukushkin, Nikolai S., 1994. "A fixed-point theorem for decreasing mappings," Economics Letters, Elsevier, vol. 46(1), pages 23-26, September.
    4. Roy, Sunanda & Sabarwal, Tarun, 2010. "Monotone comparative statics for games with strategic substitutes," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 793-806, September.
    5. Acemoglu, Daron & Jensen, Martin Kaae, 2013. "Aggregate comparative statics," Games and Economic Behavior, Elsevier, vol. 81(C), pages 27-49.
    6. Jack Hirshleifer, 1989. "Conflict and rent-seeking success functions: Ratio vs. difference models of relative success," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 251-262, Springer.
    7. 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.
    8. Martin Kolmar & Andreas Wagener, 2013. "Inefficiency As A Strategic Device In Group Contests Against Dominant Opponents," Economic Inquiry, Western Economic Association International, vol. 51(4), pages 2083-2095, October.
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    Cited by:

    1. Zenou, Yves & Xu, Jin & Zhou, Junjie, 2019. "Networks in Conflict: A Variational Inequality Approach," CEPR Discussion Papers 13647, C.E.P.R. Discussion Papers.
    2. Franke, Jörg & Metzger, Lars P., 2023. "Repeated Contests with Draws," Ruhr Economic Papers 1016, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    3. Escobar, Juan F., 2025. "Comparative statics in strategic form games," Economics Letters, Elsevier, vol. 250(C).
    4. Christian Ewerhart & Federico Quartieri, 2020. "Unique equilibrium in contests with incomplete information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(1), pages 243-271, July.
    5. Li, Bo & Wu, Zenan & Xing, Zeyu, 2023. "Optimally biased contests with draws," Economics Letters, Elsevier, vol. 226(C).
    6. Xu, Jin & Zenou, Yves & Zhou, Junjie, 2022. "Equilibrium characterization and shock propagation in conflict networks," Journal of Economic Theory, Elsevier, vol. 206(C).
    7. Adriana Gama & David Michael Rietzke, 2017. "Robust Comparative Statics in Contests," Working Papers 173174403, Lancaster University Management School, Economics Department.
    8. Emin Karagözoğlu & Kerim Keskin & Çağrı Sağlam, 2024. "Submodularity and supermodularity in contest games," International Journal of Economic Theory, The International Society for Economic Theory, vol. 20(2), pages 182-198, June.
    9. 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.
    10. Zenou, Yves & Bochet, Olivier & Faure, Mathieu & Long, Yan, 2020. "Perceived Competition in Networks," CEPR Discussion Papers 15582, C.E.P.R. Discussion Papers.
    11. Morgan, John & Tumlinson, Justin & Várdy, Felix, 2022. "The limits of meritocracy," Journal of Economic Theory, Elsevier, vol. 201(C).
    12. Bochet, Olivier & Faure, Mathieu & Long, Yan & Zenou, Yves, 2020. "Perceived Competition in Networks," CEPR Discussion Papers 15582, C.E.P.R. Discussion Papers.
    13. Jindapon, Paan & Yang, Zhe, 2017. "Risk attitudes and heterogeneity in simultaneous and sequential contests," Journal of Economic Behavior & Organization, Elsevier, vol. 138(C), pages 69-84.

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    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • E20 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - General (includes Measurement and Data)
    • I30 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - General

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