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Aggregative Games

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  • Martin K. Jensen

Abstract

An abstract notion of aggregative games is introduced and a pure strategy Nash equilibrium shown to exist for such games. Convergence of best-reply improvement dynamics is also studied. All assumptions are straight-forward to check in concrete applications. The paper’s results generalize the main results of Dubey et al. (2006) and Kukushkin (2005). Likewise, the aggregator concept of Alos-Ferrer and Ania (2005) and Schipper (2005) is a special case. The relationship with both is studied in detail. A number of examples illustrate the paper’s main findings. Among these a model of open source development may be of some independent interest.

Suggested Citation

  • Martin K. Jensen, 2006. "Aggregative Games," Discussion Papers 06-10, Department of Economics, University of Birmingham.
    • Handle: RePEc:bir:birmec:06-10
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    File URL: https://repec.cal.bham.ac.uk/pdf/06-10.pdf
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    Cited by:

    1. Kukushkin, Nikolai S., 2016. "Nash equilibrium with discontinuous utility functions: Reny's approach extended," MPRA Paper 75862, University Library of Munich, Germany.
    2. Kukushkin, Nikolai S., 2018. "Better response dynamics and Nash equilibrium in discontinuous games," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 68-78.
    3. Alex Dickson, 2017. "Multiple-aggregate games," Working Papers 1701, University of Strathclyde Business School, Department of Economics.
    4. Volker Nocke & Nicolas Schutz, 2018. "Multiproduct‐Firm Oligopoly: An Aggregative Games Approach," Econometrica, Econometric Society, vol. 86(2), pages 523-557, March.
    5. 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.
    6. Jayash Koshal & Angelia Nedić & Uday V. Shanbhag, 2016. "Distributed Algorithms for Aggregative Games on Graphs," Operations Research, INFORMS, vol. 64(3), pages 680-704, June.
    7. Acemoglu, Daron & Jensen, Martin Kaae, 2013. "Aggregate comparative statics," Games and Economic Behavior, Elsevier, vol. 81(C), pages 27-49.
    8. Dominik Erharter, 2013. "Promoting coordination in summary-statistic games," Working Papers 2013-28, Faculty of Economics and Statistics, Universität Innsbruck.

    More about this item

    Keywords

    Aggregative Games; Aggregation; Strategic Substitutes; Nash Equilibrium; Potential Game; Best-reply Dynamics;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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