Summary
This paper presents a class of games — designated as Randomly Furcating Stochastic Differential Game — in which random shocks in the stock dynamics and (future) stochastic changes in payoffs are present. Since future payoff are not known with certainty, the term “randomly furcating” is introduced to emphasize that a particularly useful way to analyze such a situation is to assume that payoffs change at any future time instant according to (known) probability distributions defined in terms of multiple-branching stochastic processes. New and significant mathematical results are obtained, under which it becomes possible to characterize the conditions under which previously unsolvable games can be solved. Two illustrations are provided.
This is a preview of subscription content, log in via an institution to check access.
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
Basar, T. (1977a): Existence of Unique Equilibrium Solutions in Nonzero-Sum Stochastic Differential Games. In: Roxin, E. O., Liu, P. T., Sternberg, R. (Eds.): Differential Games and Control Theory II. Marcel Dekker, Inc., 201 - 228
Basar, T. (1977b): Informationally Nonunique Equilibrium Solutions in Differential Games. SIAM Journal of Control and Optimization 15, 636 - 660
Basar, T. (1980b): On the Existence and Uniqueness of Closed-Loop SamledData Nash Controls in Linear-Quadratic Stochastic Differential Games. In: Iracki, K. et al. (Eds.): Optimization Techniques. Lecture Notes in Control and information Sciences. Springer-Verlag, New York, ch. 22, 193 - 203
Berkovitz, L. D. (1964): A variational approach to differential games. In: Dresher, M., Shapley, L. S., Tucker, A. W. (Eds.): Advances in Game Theory. Princeton, Princeton University Press, NJ, 127 - 174
Clark, C. W. (1976): Mathematical Bioeconomics: The Optimal Management of Renewable Resources. John Wiley, New York
Clark, C. W. (1980): Restricted assess to common-property Fishery resources: a game theoretic analysis. In: Liu, P. T. (Ed.): Dynamic Optimization and Mathematical Economics. Plenum, New York, 117 - 132
Clemhout, S., Wan, H. Y. Jr. (1985): Dynamic common-property resources and environmental problems. Journal of Optimization Theory and Applications 46, 471 - 481
Davis, M. H. A. (1984): Piecewise-deterministic markov processes: a general class of non-diffusion stochastic models. Journal of the Royal Statistical Society (B) 46, 353 - 388
Dockner, E. J., Feichtinger, G., Mehlmann, A. (1989): Noncooperative solutions for a differential game model of fishery. Journal of Economic Dynamics and Control 13, 1 - 20
Dockner, E., Jorgensen, S., Long, N. V., Sorger, G. (2000): Differential Games in Economics and Management Science. Cambridge University Press, Cambridge
Fleming, W. H. (1969): Optimal continuous-parameter stochastic control. SIAM Review 11, 470 - 509
Fleming, W. H., Rishel, R. W. (1975): Deterministic and Stochastic Optimal Control. Springer-Verlag, Berlin
Isaacs, R. (1965): Differential Games. Wiley, New York
Jorgensen, S., Yeung, D. (1996): Stochastic differential game model of a common property fishery. Journal of Optimization Theory and Applications 90, 391 - 403
Kaitala, V. (1993): Equilibria in a stochastic resource management game under imperfect information. European Journal of Operational Research 71, 439 - 453
Kamien, Schwartz (1991): Identification of classes of differential games for which the open-loop is a degenerate feedback Nash equilibrium. Journal of Optimization Theory and Applications 55, 217 - 231
Leitmann, G., Mon, G. (1967): Some geometric aspects of differential games. Journal of Astronaut and Science 14, 56
Rishel, R. (1975a): Control of systems with jump Markov disturbances. IEEE Transactions on Automatic Control 20, 241 - 244
Rishel, R. (1975b): Dynamic programming and minimum principles for systems with jump Markov disturbances. SIAM Journal of Control 13, 338 - 371
Sorger, G. (1989): Competitive dynamic advertising: a modification of the Case game. Journal of Economic Dynamics and Control 13, 55 - 80
Vermes, D. (1985): Optimal control of piecewise-deterministic Markov processes. Stockastics 14, 165 - 208
Yeung, D. W. K. (1998): A Class of Differential Games Which Admits a Feedback Solution with Linear Value Functions. European Journal of Operational Research 107 (3), 737 - 754
Yeung, D. W. K. (1999): A stochastic differential game model of institutional investor speculation. Journal of Optimization Theory and Applications 102, 463 - 477
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Yeung, D.W.K. (2003). Randomly-Furcating Stochastic Differential Games. In: Petrosyan, L.A., Yeung, D.W.K. (eds) ICM Millennium Lectures on Games. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05219-8_6
Download citation
DOI: https://doi.org/10.1007/978-3-662-05219-8_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05618-5
Online ISBN: 978-3-662-05219-8
eBook Packages: Springer Book Archive