Differential Games with Random Duration: A Hybrid Systems Formulation
Abstract
The contribution of this paper is two-fold. First, a new class of differential games with random duration and a composite cumulative distribution function is introduced. Second, it is shown that these games can be well defined within the hybrid systems framework and that the problem of finding the optimal strategy can be posed and solved with the methods of hybrid optimal control theory. An illustrative example is given.
Keywords:
games, hybrid
Downloads
Download data is not yet available.
References
Azhmyakov, V., S. A. Attia, D. Gromov, and J. Raisch (2007). Necessary optimality conditions for a class of hybrid optimal control problems. In A. Bemporad, A. Bicchi, and G. Butazzo, editors, HSCC 2007, LNCS 4416, pages 637–640. Springer-Verlag.
Bardi, M., and I. Capuzzo-Dolcetta (1997). Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations. Birkhäuser.
Boukas, E. K., A. Haurie, and P. Michel (1990). An optimal control problem with a random stopping time. Journal of optimization theory and applications, 64(3), 471–480.
Chang, F. R. (2004). Stochastic Optimization in Continuous Time. Cambridge Univ. Press.
Dockner, E. J., S. Jorgensen, N. van Long, and G. Sorger (2000). Differential Games in Economics and Management Science. Cambridge Univ. Press.
Kostyunin, S. and E. Shevkoplyas (2011). On simplification of integral payoff in differential games with random duration. Vestnik St.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 4, 47–56.
Lee, E. B and L. Markus (1967). Foundations of optimal control theory. Wiley.
Petrosyan, L. A. and N. V. Murzov (1966). Game-theoretic problems of mechanics. Litovsk. Math. Sb., 6, 423–433 (in Russian).
Petrosyan, L. A. and E. V. Shevkoplyas (2003). Cooperative solutions for games with random duration. Game Theory and Applications, IX, 125–139.
Pontryagin, L. S., V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko (1963). The Mathematical Theory of Optimal Processes. Wiley-Interscience.
Riedinger, P., C. Iung, and F. Kratz (2003). An optimal control approach for hybrid systems. European Journal of Control, 9(5), 449–458.
Royden, H. L. (1988). Real Analysis. Prentice Hall, 3rd edition.
Shaikh, M. S. and P. E. Caines (2007). On the hybrid optimal control problem: Theory and algorithms. IEEE Transactions on Automatic Control, 52(9), 1587–1603.
Vinter, R. (2000). Optimal Control. Birkhäuser.
Yaari, M. E. (1965). Uncertain lifetime, life insurance, and the theory of the consumer. The Review of Econimic Studies, 32(2), 137–150.
Zorich, V. A. (2004). Mathematical Analysis, volume II. Springer.
Downloads
Published
2022-08-09
How to Cite
Gromov, D., & Gromova, E. (2022). Differential Games with Random Duration: A Hybrid Systems Formulation. Contributions to Game Theory and Management, 7. Retrieved from https://gametheory.spbu.ru/article/view/13595
Issue
Section
Articles
License
Articles of "Contributions to Game Theory and Management" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.
