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# Externalities in the games over electrical power transmission networks

## Author

Listed:
• László Á. Kóczy

() (Óbuda University)

• Dávid Csercsik

## Abstract

An electrical transmission network consists of producers, consumers and the power lines connecting them. We build an ideal (lossless) DC load ow model as a cooperative game over a graph with the producers and consumers located at the nodes, each described by a maximum supply or desired demand and the power lines represented by the edges, each with a given power transmission capacity and admittance value describing its ability to transmit electricity. Today's transmission networks are highly interconnected, but or- ganisationally partitioned into several subnetworks, the so-called bal- ancing groups with balanced production and consumption. We study the game of balancing group formation and show that the game con- tains widespread externalities that can be both negative and positive. We study the stability of the transportation network using the recur- sive core. While the game is clearly cohesive, we demonstrate that it is not necessarily superadditive. We argue that subadditivity may be a barrier to achieve full cooperation. Finally the model is extended to allow for the extension of the underlying transmission network.

## Suggested Citation

• László Á. Kóczy & Dávid Csercsik, 2011. "Externalities in the games over electrical power transmission networks," Working Paper Series 1103, Óbuda University, Keleti Faculty of Business and Management.
• Handle: RePEc:pkk:wpaper:1103.rdf
as

File URL: http://uni-obuda.hu/users/vecseya/RePEc/pkk/wpaper/1103.pdf
File Function: Manuscript, 2011

## References listed on IDEAS

as
1. Henry Tulkens & Parkash Chander, 1997. "The Core of an Economy with Multilateral Environmental Externalities," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(3), pages 379-401.
2. Neuhoff, Karsten & Barquin, Julian & Boots, Maroeska G. & Ehrenmann, Andreas & Hobbs, Benjamin F. & Rijkers, Fieke A.M. & Vazquez, Miguel, 2005. "Network-constrained Cournot models of liberalized electricity markets: the devil is in the details," Energy Economics, Elsevier, vol. 27(3), pages 495-525, May.
3. Hobbs, Benjamin F. & Kelly, Kevin A., 1992. "Using game theory to analyze electric transmission pricing policies in the United States," European Journal of Operational Research, Elsevier, vol. 56(2), pages 154-171, January.
4. LÃ¡szlÃ³ KÃ³czy, 2007. "A recursive core for partition function form games," Theory and Decision, Springer, vol. 63(1), pages 41-51, August.
5. Kóczy, László Á., 2009. "Sequential coalition formation and the core in the presence of externalities," Games and Economic Behavior, Elsevier, vol. 66(1), pages 559-565, May.
6. Kleindorfer, Paul R. & Wu, D. -J. & Fernando, Chitru S., 2001. "Strategic gaming in electric power markets," European Journal of Operational Research, Elsevier, vol. 130(1), pages 156-168, April.
7. Gately, Dermot, 1974. "Sharing the Gains from Regional Cooperation: A Game Theoretic Application to Planning Investment in Electric Power," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 15(1), pages 195-208, February.
8. Richard Gilbert & Neuhoff, K. & Newbery, D., 2002. "Allocating Transmission to Mitigate Market Power in Electricity Networks," Cambridge Working Papers in Economics 0225, Faculty of Economics, University of Cambridge.
9. Cardell, Judith B. & Hitt, Carrie Cullen & Hogan, William W., 1997. "Market power and strategic interaction in electricity networks," Resource and Energy Economics, Elsevier, vol. 19(1-2), pages 109-137, March.
10. Yihsu Chen & Benjamin Hobbs & Sven Leyffer & Todd Munson, 2006. "Leader-Follower Equilibria for Electric Power and NO x Allowances Markets," Computational Management Science, Springer, vol. 3(4), pages 307-330, September.
Full references (including those not matched with items on IDEAS)

## Citations

### Blog mentions

As found by EconAcademics.org, the blog aggregator for Economics research:
1. Nem minden hÃ¡lÃ³zat szuper (lehet szubadditÃ­v is)
by KÃ³czy LÃ¡szlÃ³ in Kóczy játékelmélet blogja on 2011-05-30 18:18:00

### Citations

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Cited by:

1. repec:spr:thdlic:978-3-319-69841-0 is not listed on IDEAS
2. Helga Habis & Dávid Csercsik, 2015. "Cooperation with Externalities and Uncertainty," Networks and Spatial Economics, Springer, vol. 15(1), pages 1-16, March.
3. David Csercsik, 2013. "Competition and cooperation in a PFF game theoretic model of electrical energy trade," IEHAS Discussion Papers 1310, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
4. Joris Morbee, 2014. "International Transport of Captured $$\hbox {CO}_2$$ CO 2 : Who Can Gain and How Much?," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 57(3), pages 299-322, March.

### Keywords

Energy transmission networks; Coop- erative game theory; Partition function form games; Externalities;

### JEL classification:

• C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
• L14 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Transactional Relationships; Contracts and Reputation
• L94 - Industrial Organization - - Industry Studies: Transportation and Utilities - - - Electric Utilities

### NEP fields

This paper has been announced in the following NEP Reports:

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