Abstract
Several solution concepts have been defined for abstract games. Some of these are the core, due to Gillies and Shapley, the Von Neumann-Morgenstern stable sets, and the subsolutions due to Roth. These solution concepts are rather static in nature. In this paper, we propose a new solution concept for abstract games, called the dynamic solution, that reflects the dynamic aspects of negotiation among the players. Some properties of the dynamic solution are studied. Also, the dynamic solution of abstract games arising fromn-person cooperative games in characteristic function form is investigated.
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References
Gillies, D. B.,Solutions to General Nonzero-Sum Games, Annals of Mathematics Studies No. 40, Edited by A. W. Tucker and R. D. Luce, Princeton University Press, Princeton, New Jersey, 1959.
Von Neumann, J., andMorgenstern, O.,Theory of Games and Economic Behavior, Princeton University Press, Princeton, New Jersey, 1944.
Roth, A. E.,Subsolutions and the Supercore of Cooperative Games, Mathematics of Operations Research, Vol. 1, pp. 43–49, 1976.
Kalai, E., Pazner, E. A., andSchmeidler, D.,Collective Choice Correspondences as Admissible Outcomes of Social Bargaining Processes, Econometrica, Vol. 44, pp. 223–240, 1976.
Kalai, E., andSchmeidler, D.,An Admissible Set Occurring in Various Bargaining Situations, Northwestern University, Center for Mathematical Studies in Economics and Management Science, Discussion Paper No. 191, 1975.
Behzad, M., andHarary, F.,On the Problem of Characterizing Digraphs with Solutions and Kernels, Bulletin of the Iranian Mathematical Society, Vol. 3, 1975.
Behzad, M., andHarary, F.,Which Directed Graphs Have a Solution?, Mathematica Slovaca, Vol. 27, pp. 37–41, 1977.
Shmadich, K.,The Existence of Graphic Solutions, Leningrad University Herald, Vol. 1, pp. 88–92, 1976.
Lucas, W. F.,A Counterexample in Game Theory, Management Science, Vol. 13, pp. 766–767, 1967.
Lucas, W. F.,On Solutions for n-Person Games, The RAND Corporation, Research Memorandum No. RM-5567-PR, 1968.
Lucas, W. F.,A Game with No Solution, Bulletin of the American Mathematical Society, Vol. 74, pp. 237–239, 1968.
Lucas, W. F.,The Proof That a Game May Not Have a Solution, Transactions of the American Mathematical Society, Vol. 137, pp. 219–229, 1969.
Lucas, W. F.,Games with Unique Solutions That Are Nonconvex, Pacific Journal of Mathematics, Vol. 28, pp. 599–602, 1969.
Stearns, R. E.,A Game without Side Payments That Has No Solution, Princeton University, Report on the Fifth Conference on Game Theory, Edited by W. F. Lucas, 1965.
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Communicated by G. Leitmann
This research was supported by the Office of Naval Research under Contract No. N00014-75-C-0678, by the National Science Foundation under Grants Nos. MPS-75-02024 and MCS-77-03984 at Cornell University, by the United States Army under Contract No. DAAG-29-75-C-0024, and by the National Science Foundation under Grant No. MCS-75-17385-A01 at the University of Wisconsin. The author is grateful to Professor W. F. Lucas under whose guidance the research was conducted.
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Shenoy, P.P. A dynamic solution concept for abstract games. J Optim Theory Appl 32, 151–169 (1980). https://doi.org/10.1007/BF00934721
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DOI: https://doi.org/10.1007/BF00934721