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Network of Commons

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  • Rahmi Ilkiliç

    (Maastricht University)

Abstract

A tragedy of the commons appears when the users of a common resource have incentives to exploit it more than the socially efficient level. We analyze the situation when the tragedy of the commons is embedded in a network of users and sources. Users play a game of extractions, where they decide how much resource to draw from each source they are connected to. We show that if the value of the resource to the users is linear, then each resource exhibits an isolated problem. There exists a unique equilibrium. But when the users have concave values, the network structure matters. The exploitation at each source depends on the centrality of the links connecting the source to the users. The equilibrium is unique and we provide a formula which expresses the quantities at an equilibrium as a function of a network centrality measure. Next we characterize the efficient levels of extractions by users and outflows from sources. Again, the case of linear values can be broken down source by source. For the case of concave values, we provide a graph decomposition which divides the network into regions according to the availability of sources. Then the efficiency problem can be solved region by region.

Suggested Citation

  • Rahmi Ilkiliç, 2008. "Network of Commons," Working Papers 2008.30, Fondazione Eni Enrico Mattei.
    • Handle: RePEc:fem:femwpa:2008.30
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    References listed on IDEAS

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    6. Nicolas Faysse, 2005. "Coping With The Tragedy Of The Commons: Game Structure And Design Of Rules," Post-Print cirad-01002167, HAL.
    7. Corominas-Bosch, Margarida, 2004. "Bargaining in a network of buyers and sellers," Journal of Economic Theory, Elsevier, vol. 115(1), pages 35-77, March.
    8. H. Scott Gordon, 1954. "The Economic Theory of a Common-Property Resource: The Fishery," Palgrave Macmillan Books, in: Chennat Gopalakrishnan (ed.), Classic Papers in Natural Resource Economics, chapter 9, pages 178-203, Palgrave Macmillan.
    9. Nicolas Faysse, 2005. "Coping with the Tragedy of the Commons: Game Structure and Design of Rules," Journal of Economic Surveys, Wiley Blackwell, vol. 19(2), pages 239-261, April.
    10. Yukihiko Funaki & Takehiko Yamato, 1999. "The core of an economy with a common pool resource: A partition function form approach," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(2), pages 157-171.
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    Cited by:

    1. Hernández, Penélope & Muñoz-Herrera, Manuel & Sánchez, Ángel, 2013. "Heterogeneous network games: Conflicting preferences," Games and Economic Behavior, Elsevier, vol. 79(C), pages 56-66.

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    More about this item

    Keywords

    Tragedy of The Commons; Networks; Nash Equilibrium; Efficiency; Centrality Measures;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation
    • Q20 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - General

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