Abstract
In this paper the definition of cooperative game in characteristic function form is given. The notions of optimality principle and solution concepts based on it are introduced. The new concept of “imputation distribution procedure” (IDP) is defined and connected with the basic definitions of time-consistency and strong time-consistency. Sufficient conditions of the existence of time-consistent solutions are derived. For a large class of games where these conditions cannot be satisfied, the regularization procedure is developed and new c.f. constructed. The “regularized” core is defined and its strong time-consistency proved.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Filar, J., Petrosjan, L.A., Dynamic Cooperative Games, International Game Theory Review, Vol. 2, No. 1 42–65, 2000.
Haurie, A., On Some Properties of the Characteristic Function and Core of Multistage Game of Coalitions, IEEE Transaction on Automatic Control 236–241, April 1975.
Strotz, K. H., Myopia and Inconsistency in Dynamic Utility Maximization, Review of Economic Studies, Vol 23, 1955–1956.
Petrosjan, L.A., The Shapley Value for Differential Games, New Trends in Dynamic Games and Applications, Geert Olsder ed., Birkhauser, 409–417, 1995.
Petrosjan, L.A., Differential Games of Pursuit, World Scientific, London 1993.
Bellman, R.E., Dynamic Programming, Princeton University Press, Princeton, NJ, 1957.
Haurie, A., A Note on Nonzero-Sum Differential Games with Bargaining Solution, Journal of Optimization Theory and Application, Vol 18.1 31–39, 1976.
Kaitala, V., Pohjola, M., Optimal Recovery of a Shared Resource Stock. A Differential Game Model with Efficient Memory Equilibria, Natural Resource Modeling, Vol. 3.1 191–199, 1988.
Petrosjan, L.A., Danilov N.N., Cooperative Differential Games, Tomsk University Press 276, 1985.
Petrosjan, L.A., Danilov N.N., Stability of Solution in Nonzero-Sum Differential Games with Transferable Payoffs, Vestnik of Leningrad University, No. 1 52–59, 1979.
Petrosjan, L.A., On the Time-Consistency of the Nash Equilibrium in Multistage Games with Discount Payoffs, Applied Mathematics and Mechanics (ZAMM), Vol. 76Supplement 3 535–536, 1996.
Petrosjan, L.A., Zaccour, G., Time-Consistent Shapley Value Allocation of Pollution Cost Reduction, Journal of Economic Dynamics and Control, Vol. 27, 381–398, 2003.
McKinsey, Introduction to the Theory of Games, McGraw-Hill, NY, 1952.
Owen, G. Game Theory, W.B. Saunders Co., Philadelphia, 1968.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Birkhäuser Boston
About this chapter
Cite this chapter
Petrosjan, L.A. (2005). Cooperative Differential Games. In: Nowak, A.S., Szajowski, K. (eds) Advances in Dynamic Games. Annals of the International Society of Dynamic Games, vol 7. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4429-6_9
Download citation
DOI: https://doi.org/10.1007/0-8176-4429-6_9
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4362-1
Online ISBN: 978-0-8176-4429-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)