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Two‐Aggregate Games: Demonstration Using a Production–Appropriation Model

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  • Richard Cornes
  • Roger Hartley
  • Yuji Tamura

Abstract

We expand the scope of the two‐aggregate method by applying it to a situation in which many heterogeneous players are free to contribute to both aggregates. Such situations naturally arise in various resource allocation problems. Hence, our method is useful in many applications. A production–appropriation model is employed to illustrate how the problem of establishing the Nash equilibrium can be reduced from solving n>2 best‐response functions in n unknowns to solving two consistency conditions in two unknowns. We then conduct a comparative static exercise that the conventional approach could not handle easily, if at all, to demonstrate the power of our method.

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  • Richard Cornes & Roger Hartley & Yuji Tamura, 2019. "Two‐Aggregate Games: Demonstration Using a Production–Appropriation Model," Scandinavian Journal of Economics, Wiley Blackwell, vol. 121(1), pages 353-378, January.
    • Handle: RePEc:bla:scandj:v:121:y:2019:i:1:p:353-378
    DOI: 10.1111/sjoe.12257
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    Cited by:

    1. Dripto Bakshi & Indraneel Dasgupta, 2021. "A Subscription vs. Appropriation Framework for Natural Resource Conflicts," World Scientific Book Chapters, in: Anil Markandya & Dirk Rübbelke (ed.), CLIMATE AND DEVELOPMENT, chapter 9, pages 257-307, World Scientific Publishing Co. Pte. Ltd..
    2. Richard Cornes & Roger Hartley & Yuji Tamura, 2019. "Two‐Aggregate Games: Demonstration Using a Production–Appropriation Model," Scandinavian Journal of Economics, Wiley Blackwell, vol. 121(1), pages 353-378, January.
    3. Luis C. Corchón, 2021. "Aggregative games," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 12(1), pages 49-71, March.

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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

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