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.
partition function form games uncertainty core sustainability networks game theory externalities
Aumann RJ, Peleg B (1960) Von Neumann-Morgenstern solutions to cooperative games without side payments. Bull Am Math Soc 66:173–179CrossRefGoogle 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.2010.2043749Google Scholar
Chander P, Tulkens H (1997) The core of and economy with multilateral environmental externalities. Int J Game Theory 26(3):379–401CrossRefGoogle 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 47–85Google Scholar
Habis H, Herings PJJ (2011a) Core concepts for incomplete market economies. J Math Econ 47(4–5):595–609CrossRefGoogle 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:1023907818360CrossRefGoogle Scholar
Moulin H (1985) The separability axiom and equal sharing methods. J Econ Theory 36 (1):120–148CrossRefGoogle 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 38:465–482CrossRefGoogle Scholar