Skip to main content
SpringerLink
Log in

Cooperation with Externalities and Uncertainty

  • Published:
Networks and Spatial Economics Aims and scope Submit manuscript

Abstract

We introduce a new solution concept to problems with externalities, which is the first in the literature to take into account economic, regulatory and physical stability aspects of network problems in the very same model. A new class of cooperative games is defined where the worth of a coalition depends on the behavior of other players and on the state of nature as well. We allow for coalitions to form both before and after the resolution of uncertainty, hence agreements must be stable against both types of deviations. The appropriate extension of the classical core concept, the Sustainable Core, is defined for this new setup to test the stability of allocations in such a complex environment.

A prominent application, a game of consumers and generators on an electrical energy transmission network is examined in details, where the power in- and outlets of the nodes have to be determined in a way, that if any line instantaneously fails, none of the remaining lines may be overloaded. We show that fulfilling this safety requirement in a mutually acceptable way can be achieved by choosing an element in the Sustainable Core.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Notes

  1. Further desirable properties are discussed in Kóczy (2006).

References

  • Abrell J, Weigt H (2012) Combining energy networks. Netw Spat Econ 12(3):377–401. doi:10.1007/s11067-011-9160-0

    Article  Google Scholar 

  • Aumann RJ, Peleg B (1960) Von Neumann-Morgenstern solutions to cooperative games without side payments. Bull Am Math Soc 66:173–179

    Article  Google Scholar 

  • Beccuti A, Demiray T, Andersson G, Morari M (2010) A lagrangian decomposition algorithm for optimal emergency voltage control. Power Systems. IEEE Trans 25(4):1769–1779. doi:10.1109/TPWRS.2010.2043749

    Google Scholar 

  • Chander P, Tulkens H (1997) The core of and economy with multilateral environmental externalities. Int J Game Theory 26(3):379–401

    Article  Google Scholar 

  • Chen B, Lam W, Sumalee A, Li Q, Shao H, Fang Z (2013) Finding reliable shortest paths in road networks under uncertainty. Netw Spat Econ 13(2):123–148. doi:10.1007/s11067-012-9175-1

    Article  Google Scholar 

  • Contreras J (1997) A cooperative game theory approach to transmission planning in power systems. PhD thesis. University of California, Berkeley

    Google Scholar 

  • Csercsik D, Kóczy LÁ (2011) Externalities in the games over electrical power transmission networks. IEHAS Discussion Papers 1125, Institute of Economics. Hungarian Academy of Sciences, Budapest. http://econ.core.hu/file/download/mtdp/MTDP1125.pdf

    Google Scholar 

  • Ehrenmann A (2004) Equilibrium problems with equilibrium constraints and their application to electricity markets. Fitzwilliam College, Fitzwilliam 154

  • Fairley P (2004) The unruly power grid. IEEE Spectr 41:22–27

    Google Scholar 

  • Gabriel S, Kiet S, Balakrishnan S (2004) A mixed integer stochastic optimization model for settlement risk in retail electric power markets. Netw Spat Econ 4(4):323–345. doi:10.1023/B:NETS.0000047111.94897.d4

    Article  Google Scholar 

  • Gillies DB (1959) Solutions to General Non-zero-sum Games. In: Tucker A W, Luce R D (eds) Contributions to the Theory of Games IV, No. 40 in Annals of Mathematics Studies. Princeton University Press, Princeton, pp 47–85

    Google Scholar 

  • Habis H, Herings PJJ (2011a) Core concepts for incomplete market economies. J Math Econ 47(4–5):595–609

    Article  Google Scholar 

  • Habis H, Herings PJJ (2011b) Transferable utility games with uncertainty. J Econ Theory 146(5):2126–2139. http://ideas.repec.org/a/eee/jetheo/v146y2011i5p2126-2139.html

    Article  Google Scholar 

  • Hines P, Apt J, Talukdar S (2009) Large blackouts in North America: Historical trends and policy implications. Energy Policy 37(12):5249–5259. doi:10.1016/j.enpol.2009.07.049. http://www.sciencedirect.com/science/article/pii/S0301421509005667

    Article  Google Scholar 

  • Kaltenbach J, Hajdu L (1971) Optimal corrective rescheduling for power system security. IEEE Trans Power Appar Syst 90:843–851

    Article  Google Scholar 

  • Kleindorfer P, Wu DJ, Fernando C (2001) Strategic gaming in electric power markets. Eur J Oper Res 130:156–168

    Article  Google Scholar 

  • Kóczy LÁ (2006) A recursive core for partition function form games. Research Memorandum RM/06/031, METEOR. Maastricht University, Maastricht

    Google Scholar 

  • Kóczy LÁ (2007) A recursive core for partition function form games. Theory Decis 63(1):41–51. doi:10.1007/s11238-007-9030-x

    Article  Google Scholar 

  • Leuthold F, Weigt H, von Hirschhausen C (2012) A large-scale spatial optimization model of the european electricity market. Netw Spat Econ 12(1):75–107. doi:10.1007/s11067-010-9148-1

    Article  Google Scholar 

  • Li ZC, Lam W, Wong S (2009) The optimal transit fare structure under different market regimes with uncertainty in the network. Netw Spat Econ 9(2):191–216. doi:10.1007/s11067-007-9058-z

    Article  Google Scholar 

  • Metzler C, Hobbs B, Pang JS (2003) Nash-Cournot equilibria in power markets on a linearized dc network with arbitrage: Formulations and properties. Netw Spat Econ 3(2):123–150. doi:10.1023/A:1023907818360

    Article  Google Scholar 

  • Moulin H (1985) The separability axiom and equal sharing methods. J Econ Theory 36 (1):120–148

    Article  Google Scholar 

  • Oggioni G, Smeers Y, Allevi E, Schaible S (2012) A generalized Nash equilibrium model of market coupling in the european power system. Netw Spat Econ 12(4):503–560. doi:10.1007/s11067-011-9166-7

    Article  Google Scholar 

  • Oren S, Spiller P, Varaiya P, Wu F (1995) Folk theorems on transmission access: Proofs and counter examples. Working papers series of the Program on Workable Energy Regulation (POWER) PWP-023, University of California Energy Institute 2539 Channing Way Berkeley, California 94720–5180 . http://www.ucei.berkeley.edu/ucei

  • Predtetchinski A, Herings PJJ, Peters H (2002) The strong sequential core for two-period economies. J Math Econ 38:465–482

    Article  Google Scholar 

  • Ray D (1989) Credible coalitions and the core. Int J Game Theory 18:185–187

    Article  Google Scholar 

  • Ray D, Vohra R (1997) Equilibrium binding agreements. J Econ Theory 73(1):30–78

    Article  Google Scholar 

  • Shenoy PP (1980) A dynamic solution concept for abstract games. J Optim Theory Appl 32(2):151–169

    Article  Google Scholar 

  • Smeers Y (2003) Market incompleteness in regional electricity transmission. part ii: The forward and real time markets. Netw Spat Econ 3(2):175–196. doi:10.1023/A:1023916120177

    Article  Google Scholar 

  • Thanikachalam A, Tudor J (1971) Optimal rescheduling of power for system reliability. Power Appar Syst IEEE Trans PAS- 90(5):2186–2192. doi:10.1109/TPAS.1971.293039

    Article  Google Scholar 

  • Thrall RM, Lucas WF (1963) n-person games in partition function form. Naval Res Logist Q 10(4):281–298

    Article  Google Scholar 

  • De la Torre S, Conejo A, Contreras J (2003) Simulating oligopolistic pool-based electricity markets: A multiperiod approach. Power Syst IEEE Trans 18(4):1547–1555

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Economics, Lund University, P.O. Box 7082, S-220 07, Lund, Sweden

    Helga Habis

  2. Faculty of Information Technology and Bionics, Pázmány Péter Catholic University, Práter U. 50/A, 1083, Budapest, Hungary

    Dávid Csercsik

  3. Centre for Economic and Regional Studies of the Hungarian Academy of Sciences, Game Theory Research Group, Budaörsi U. 45, 1112, Budapest, Hungary

    Dávid Csercsik

Authors
  1. Helga Habis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dávid Csercsik
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dávid Csercsik.

Additional information

This work was supported by the Hungarian Academy of Sciences under its Momentum Programme (LP-004/2010), by the fund KAP-1.2-14/001, and by the Hungarian National Fund (OTKA NF-104706, PD-101106). The authors thak László Á. Kóczy for the helpful discussions.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Habis, H., Csercsik, D. Cooperation with Externalities and Uncertainty. Netw Spat Econ 15, 1–16 (2015). https://doi.org/10.1007/s11067-014-9265-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11067-014-9265-3

Keywords

Search

Navigation