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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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    File URL: https://www.le.ac.uk/economics/research/RePEc/lec/leecon/dp15-16.pdf
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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. Adriana Gama & David Michael Rietzke, 2017. "Robust Comparative Statics in Contests," Working Papers 173174403, Lancaster University Management School, Economics Department.

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    More about this item

    Keywords

    Comparative statics; Uniqueness; Existence; Contest; Rent-seeking; Aggregative game; Local solvability condition.;
    All these keywords.

    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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