Abstract
This paper addresses the issue of computation of the characteristic function values in a n-player linear-state cooperative differential game. One shows that the characteristic functions coincide under two different definitions of the strategic strength of coalitions. An illustrative example drawn from environmental economics is provided.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
PETROSJAN, L., and ZACCOUR, G., Time-Consistent Shapley Value of Pollution Cost Reduction, Journal of Economic Dynamics and Control, Vol. 27, pp. 381-398, 2003.
DOCKNER, E. J., JO/RGENSEN, S., VAN LONG, N., and SORGER, G., Differential Games in Economics and Management Science, Cambridge University Press, Cambridge, United Kingdom, 2000.
DOCKNER, E. J., and VAN LONG, N., International Pollution Control: Cooperative versus Noncooperative Strategies, Journal of Environmental Economics, Vol. 24, pp. 13-29, 1993.
VAN DER PLOEG, F., and DE ZEEUW, A.J., International Aspects of Pollution Control, Environmental and Resource Economics, Vol. 2, pp. 117-139, 1992.
JO/RGENSEN, S., and ZACCOUR, G., Time-Consistent Side Payment in a Dynamic Game of Downstream Pollution, Journal of Economic Dynamics and Control, Vol. 25, pp. 1973-1987, 2001.
JO/RGENSEN, S., and ZACCOUR, G., Incentive Equilibrium Strategies and Welfare Allocation in a Dynamic Game of Pollution Control, Automatica, Vol. 37, pp. 29-36, 2000.
MARTIN, E. W., PATRICK, R. H., and TOLWINSKI, B., A Dynamic Game of Transboundary Pollutant with Asymmetric Players, Journal of Environmental Economics and Management, Vol. 24, pp. 1-12, 1993.
LIST, J. A., and MASON, C. F., Optimal Institutional Arrangements for Transboundary Pollutants in a Second-Best World: Evidence from a Differential Game with Asymmetric Players, Journal of Environmental Economics and Management, Vol. 42, pp. 277-296, 2001.
KAITALA, V., and POHJOLA, M., Sustainable International Agreements on Greenhouse Warming: A Game Theory Study, Annals of the International Society of Dynamic Games, Vol. 2, pp. 67-87, 1995.
J. A. FILAR P. S. GAERTNER (1997) ArticleTitleA Regional Allocation of World CO2 Emission Reductions Mathematics and Computers in Simulation. 43 269–275
GERMAIN, M., TOINT, P., TULKENS, H., and DE ZEEUW, A.J., Transfers to Sustain Core-Theoretic Cooperation in International Stock Pollutant Control, Climate Change, International Negotiations and Belgian Strategies (CLIMNEG Network), Working Paper 6, 1998.
CHANDER, P., TULKENS, H., VAN YPERSELE, J. P., and WILLEMS, S., The Kyoto Protocol: An Economic and Game Theoretic Interpretation, Climate Change, International Negotiations and Belgian Strategies (CLIMNEG Network), Working Paper 12, 1999.
PETROSJAN, L., and ZACCOUR, G., A Multistage Supergame of Downstream Pollution, Annals of the International Society of Dynamic Games, Vol. 5, pp. 387-404, 2000.
BAHN, O., HAURIE, A., KYPREOS, S., and VIAL, J.P., Advanced Mathematical Programming Modeling to Assess the Benefits of International CO 2 Abatement Cooperation, Environmental Modeling and Assessment, Vol. 3, pp. 107-116, 1998.
BRETON, M., FREDJ, K., and ZACCOUR, G., Characteristic Functions, Coalitions Stability, and Free-Riding in a Game of Pollution Control, Les Cahiers du GERAD, Report G-2001-57, 2001.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Zaccour, G. Computation of Characteristic Function Values for Linear-State Differential Games. Journal of Optimization Theory and Applications 117, 183–194 (2003). https://doi.org/10.1023/A:1023612725533
Issue Date:
DOI: https://doi.org/10.1023/A:1023612725533