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Fully Aggregative Games

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  • Richard Cornes

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  • Roger Hartley

Abstract

A game is fully aggregative if payoffs and marginal payoffs depend only on a player's own strategy and a function of the strategy profile which is common to all players. We characterize the form which this function must take in such a game and show that the game will be strategically equivalent to another game in which the function is the simple sum of strategies.

Suggested Citation

  • Richard Cornes & Roger Hartley, 2009. "Fully Aggregative Games," ANU Working Papers in Economics and Econometrics 2009-505, Australian National University, College of Business and Economics, School of Economics.
  • Handle: RePEc:acb:cbeeco:2009-505
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    File URL: https://www.cbe.anu.edu.au/researchpapers/econ/wp505.pdf
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    References listed on IDEAS

    as
    1. Richard Cornes & Roger Hartley, 2002. "Joint Production Games with Mixed Sharing Rules," Keele Economics Research Papers KERP 2002/16, Centre for Economic Research, Keele University.
    2. 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.
    3. Novshek, William, 1984. "Finding All n-Firm Cournot Equilibria," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(1), pages 61-70, February.
    4. 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.
    5. William Novshek, 1985. "On the Existence of Cournot Equilibrium," Review of Economic Studies, Oxford University Press, vol. 52(1), pages 85-98.
    6. Richard Cornes, 1993. "Dyke Maintenance and Other Stories: Some Neglected Types of Public Goods," The Quarterly Journal of Economics, Oxford University Press, vol. 108(1), pages 259-271.
    7. Kukushkin, Nikolai S., 1994. "A fixed-point theorem for decreasing mappings," Economics Letters, Elsevier, vol. 46(1), pages 23-26, September.
    8. Richard Cornes & Roger Hartley, 2007. "Aggregative Public Good Games," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 9(2), pages 201-219, April.
    9. Corchon, Luis C., 1994. "Comparative statics for aggregative games the strong concavity case," Mathematical Social Sciences, Elsevier, vol. 28(3), pages 151-165, December.
    10. Xavier Vives, 2001. "Oligopoly Pricing: Old Ideas and New Tools," MIT Press Books, The MIT Press, edition 1, volume 1, number 026272040x, January.
    11. Novshek, William & Sonnenschein, Hugo, 1978. "Cournot and Walras equilibrium," Journal of Economic Theory, Elsevier, vol. 19(2), pages 223-266, December.
    12. Cornes, Richard & Hartley, Roger, 2003. "Risk Aversion, Heterogeneity and Contests," Public Choice, Springer, vol. 117(1-2), pages 1-25, October.
    13. Phlips,Louis, 1995. "Competition Policy," Cambridge Books, Cambridge University Press, number 9780521498715, May.
    14. A. Michael Spence, 1980. "Notes on Advertising, Economies of Scale, and Entry Barriers," The Quarterly Journal of Economics, Oxford University Press, vol. 95(3), pages 493-507.
    15. Okuguchi, Koji, 1993. "Unified approach to Cournot models : Oligopoly, taxation and aggregate provision of a pure public good," European Journal of Political Economy, Elsevier, vol. 9(2), pages 233-245, May.
    16. Yarrow, G K, 1985. "Welfare Losses in Oligopoly and Monopolistic Competition," Journal of Industrial Economics, Wiley Blackwell, vol. 33(4), pages 515-529, June.
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    Citations

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    Cited by:

    1. Possajennikov, Alex, 2015. "Conjectural variations in aggregative games: An evolutionary perspective," Mathematical Social Sciences, Elsevier, vol. 77(C), pages 55-61.
    2. Alex Dickson, 2017. "Multiple-aggregate games," Working Papers 1701, University of Strathclyde Business School, Department of Economics.
    3. Acemoglu, Daron & Jensen, Martin Kaae, 2013. "Aggregate comparative statics," Games and Economic Behavior, Elsevier, vol. 81(C), pages 27-49.
    4. Richard Cornes & Jun-ichi Itaya, 2016. "Alternative Objectives in an Oligopoly Model: An Aggregative Game Approach," CESifo Working Paper Series 6191, CESifo Group Munich.
    5. Richard Cornes, 2016. "Aggregative Environmental Games," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 63(2), pages 339-365, February.
    6. Simon P. Anderson, Nisvan Erkal and, 2009. "Aggregative Oligopoly Games with Entry," Department of Economics - Working Papers Series 1175, The University of Melbourne, revised 2013.
    7. Finn Christensen, 2016. "Comparative Statics and Heterogeneity," Working Papers 2016-01, Towson University, Department of Economics, revised Oct 2016.
    8. Massimo Motta & Emanuele Tarantino, 2017. "The effect of horizontal mergers, when firms compete in prices and investments," Economics Working Papers 1579, Department of Economics and Business, Universitat Pompeu Fabra.
    9. repec:eee:ecolet:v:163:y:2018:i:c:p:126-129 is not listed on IDEAS
    10. Nocetti, Diego & Smith, William T., 2015. "Changes in risk and strategic interaction," Journal of Mathematical Economics, Elsevier, vol. 56(C), pages 37-46.
    11. Okumura, Yasunori, 2015. "Existence of free entry equilibrium in aggregative games with asymmetric agents," Economics Letters, Elsevier, vol. 127(C), pages 14-16.
    12. Nava Kahana & Doron Klunover, 2017. "Sequential Lottery Contests with Multiple Participants," Working Papers tax-mpg-rps-2017-02, Max Planck Institute for Tax Law and Public Finance.

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    JEL classification:

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

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