Abstract
Subgame consistency is a fundamental element in the solution of cooperative stochastic differential games. In particular, it ensures that the extension of the solution policy to a later starting time and any possible state brought about by prior optimal behavior of the players will remain optimal. Recently, mechanisms for the derivation of subgame consistent solutions in stochastic cooperative differential games with transferable payoffs have been found. In the case when players’ payoffs are nontransferable, the derivation of solution candidates is extremely complicated and often intractable. In this chapter, subgame consistent solutions are derived for a class of cooperative stochastic differential games with nontransferable payoffs.
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References
Bellman, R., Dynamic Programming, Princeton University Press, Princeton, NJ, 1957.
Dockner, E.J., and Jørgensen, S., Cooperative and Non-Cooperative Differential Game Solutions to an Investment and Pricing Problem, The Journal of the Operational Research Society, 35, 8, 731–739, 1984.
Fleming, W.H., Optimal Continuous-Parameter Stochastic Control, SIAM Review, 11, 470–509, 1969.
Haurie, A., A Note on Nonzero-Sum Differential Games with Bargaining Solution, Journal of Optimization Theory and Applications, 18, 31–39, 1976.
Haurie, A., Krawczyk, J. B., and Roche, M., Monitoring Cooperative Equilibria in a Stochastic Differential Game, Journal of Optimization Theory and Applications, 81, 79–95, 1994.
Isaacs, R., Differential Games, Wiley, New York, NY, 196
Leitmann, G., Cooperative and Non-Cooperative Many Players Differential Games, Springer-Verlag, New York, NY, 1974.
Nash, J.F., Two-Person Cooperative Games, Econometrica, 21, 128–140, 1953.
Petrosyan, L.A., Stable Solutions of Differential Games with Many Participants, Viestnik of Leningrad University, 19, 46–52, 1977.
Petrosyan, L.A., Agreeable Solutions in Differential Games, International Journal of Mathematics, Game Theory and Algebra, 7, 165–177, 1997.
Petrosyan, L.A., Bargaining in Dynamic Games, ICM Millennium Lectures on Games, Edited by L. Petrosyan and D. Yeung, Springer-Verlag, Berlin, Germany, pp. 139–143, 2003.
Petrosyan, L., and Danilov, N., Stability of Solutions in Non-zero Sum Differential Games with Transferable Payoffs, Viestnik of Leningrad Universtiy, 1, 52–59, 1979.
Shapley, L.S., A Value for N-Person Games, Contributions to the Theory of Games, Edited by H.W. Kuhn and A.W. Tucker, Princeton University Press, Princeton, NJ, vol. 2, pp. 307–317, 1953.
Yeung, D.W.K., Nontransferable Individual Payoff Functions Under Stochastic Dynamic Cooperation, International Game Theory Review, 6, 2, 281–289, 2004.
Yeung, D.W.K., and Petrosyan, L.A., ProportionalTime-Consistent Solutions in Differential Games, International Conference on Logic, Game Theory and Social Choice, St. Petersburg, Russia, pp. 254–256, 2001.
Yeung, D.W.K., and Petrosyan, L.A., Subgame Consistent Cooperative Solutions in Stochastic Differential Games, Journal of Optimization Theory and Applications, 120, 3, 651–666, 2004.
Yeung, D.W.K., and Petrosyan, L.A., Subgame Consistent Solution of a Cooperative Stochastic Differential Game with Nontransferable Payoffs, forthcoming in Journal of Optimization Theory and Applications, 124, 3, 701–724, 2005.
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Yeung, D.K., Petrosyan, L., Yeung, P.M. (2007). Subgame Consistent Solutions for a Class of Cooperative Stochastic Differential Games with Nontransferable Payoffs. In: Jørgensen, S., Quincampoix, M., Vincent, T.L. (eds) Advances in Dynamic Game Theory. Annals of the International Society of Dynamic Games, vol 9. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4553-3_8
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DOI: https://doi.org/10.1007/978-0-8176-4553-3_8
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