Network of Commons
AbstractA 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Fondazione Eni Enrico Mattei in its series Working Papers with number 2008.30.
Date of creation: Mar 2008
Date of revision:
Tragedy of The Commons; Networks; Nash Equilibrium; Efficiency; Centrality Measures;
Find related papers by 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-08-06 (All new papers)
- NEP-ENV-2008-08-06 (Environmental Economics)
- NEP-GTH-2008-08-06 (Game Theory)
- NEP-NET-2008-08-06 (Network Economics)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Coralio Ballester & Antoni Calvó-Armengol & Yves Zenou, 2004.
"Who's Who in Networks. Wanted: The Key Player,"
178, Barcelona Graduate School of Economics.
- Ballester, Coralio & Calvó-Armengol, Antoni & Zenou, Yves, 2005. "Who’s Who in Networks. Wanted: The Key Player," CEPR Discussion Papers 5329, C.E.P.R. Discussion Papers.
- Coralio Ballester & Antoni Calvo-Armengol & Yves Zenou, 2005. "Who's Who in Networks. Wanted: the Key Player," NajEcon Working Paper Reviews 666156000000000586, www.najecon.org.
- Weitzman, Martin L., 1974. "Free access vs private ownership as alternative systems for managing common property," Journal of Economic Theory, Elsevier, vol. 8(2), pages 225-234, June.
- H. Scott Gordon, 1954. "The Economic Theory of a Common-Property Resource: The Fishery," Journal of Political Economy, University of Chicago Press, vol. 62, pages 124.
- 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, vol. 28(2), pages 157-171.
- Paul Seabright, 1993. "Managing Local Commons: Theoretical Issues in Incentive Design," Journal of Economic Perspectives, American Economic Association, vol. 7(4), pages 113-134, Fall.
- Penelope Hernandez & Edson Manuel Muñoz Herrera & Angel Sanchez, 2011.
"Heterogeneous Network Games: Conflicting Preferences,"
Discussion Papers in Economic Behaviour
0411, University of Valencia, ERI-CES.
- Hernández, Penélope & Muñoz-Herrera, Manuel & Sánchez, Ángel, 2013. "Heterogeneous network games: Conflicting preferences," Games and Economic Behavior, Elsevier, vol. 79(C), pages 56-66.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (barbara racah).
If references are entirely missing, you can add them using this form.