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Joint Production Games with Mixed Sharing Rules

Author

Listed:
  • Richard Cornes

    (School of Economics, University of Nottingham,)

  • Roger Hartley

    (Keele University Department of Economics)

Abstract

We study Nash equilibria of joint production games under a mixed output sharing rule in which part of the output (the mixing parameter) is shared in proportion to inputs and the rest according to exogenously determined shares. This rule includes proportional sharing and equal sharing as special cases. We show that this game has a unique equilibrium and discuss comparative statics. When the game is large, players unanimously prefer the same value of the mixing parameter: the equilibrium value of the elasticity of production. For this value, equilibrium input and output are fully efficient. Our approach exploits the fact that payoffs in the joint production game are a function only of a player’s input and the aggregate input and has independent interest as it readily extends to other ‘‘aggregative games’’.

Suggested Citation

  • 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.
    • Handle: RePEc:kee:kerpuk:2002/16
    Note: The work of the first author was supported by a Leverhulme Research Fellowship. We would like to thank Wolfgang Buchholz, Jurgen Eichberger, Gauthier Lanot, Todd Sandler, Henry Tulkens and members of seminars at the University of Melbourne and the Australian National University for helpful and encouraging comments on earlier drafts.
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    File URL: http://www.keele.ac.uk/depts/ec/wpapers/kerp0216.pdf
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    Cited by:

    1. Dickson, Alex & Hartley, Roger, 2008. "The strategic Marshallian cross," Games and Economic Behavior, Elsevier, vol. 64(2), pages 514-532, November.
    2. María Cubel & Santiago Sanchez-Pages, 2020. "Property Out of Conflict: A Survey and Some New Results," Revue d'économie politique, Dalloz, vol. 130(6), pages 891-927.
    3. Richard Cornes, 2016. "Aggregative Environmental Games," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 63(2), pages 339-365, February.
    4. Omkar D. Palsule-Desai, 2016. "Impact of equity and equality on stability and collusion in a decentralized network," Annals of Operations Research, Springer, vol. 238(1), pages 411-447, March.
    5. Omkar D. Palsule-Desai, 2015. "Complete Versus Partial Collusion in Competing Coalitions," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 17(01), pages 1-43.
    6. A. Dickson & R. Hartley, 2005. "The strategic Marshallian cross and bilateral oligopoly," Economics Discussion Paper Series 0523, Economics, The University of Manchester.
    7. Omkar Palsule-Desai, 2016. "Impact of equity and equality on stability and collusion in a decentralized network," Annals of Operations Research, Springer, vol. 238(1), pages 411-447, March.
    8. Cornes, Richard & Hartley, Roger, 2012. "Fully aggregative games," Economics Letters, Elsevier, vol. 116(3), pages 631-633.
    9. R Cornes & R Hartley, 2005. "The Geometry of Aggregative Games," Economics Discussion Paper Series 0514, Economics, The University of Manchester.

    More about this item

    Keywords

    Production externalities; non-cooperative games;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • H42 - Public Economics - - Publicly Provided Goods - - - Publicly Provided Private Goods

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