Carathéodory's method for a class of dynamic games

Journal of Mathematical Analysis and Applications

Volumn 276, Issue 2, 2002, Pages 561-588

  Carlson, Dean A ^a  

^a UNIVERSITY OF TOLEDO   (United States)

Author keywords

Carath odory's method; Dynamic games; Dynamic programming; Infinite horizon; Overtaking Nash equilibrium

Indexed keywords

EID: 0037115960     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-247X(02)00276-7     Document Type: Article

References (19)

1. T. Başar, G. Olsder, Dynamic Noncooperative Game Theory, 2nd ed., in: Classics in Applied Mathematics, Vol. 23, SIAM Publications, Philadelphia, PA, 1998.
2. L.D. Berkovitz, A theory of differential games, in: T. Başar, A. Haurie (Eds.), Advances in Dynamic Games and Applications, Birkhäuser, Boston, MA, 1994, pp. 3-22.
3. T.F. Bridgeland, On the existence of optimal feedback controls, SIAM J. Control 1 (1963) 261-274.
4. C. Carathéodory, Calculus of Variations Partial Differential Equations, Chelsea, New York, 1982.
5. D.A. Carlson, A. Haurie, A. Leizarowitz, Infinite Horizon Optimal Control: Deterministic and Stochastic Systems, 2nd ed., Springer-Verlag, New York, 1991.
6. D.A. Carlson, A. Haurie, A turnpike theory for infinite horizon open-loop differential games with decoupled controls, in: G.J. Olsder (Ed.), New Trends in Dynamic Games and Applications, in: Annals of the International Society of Dynamic Games, Birkhäuser, Boston, MA, 1995, pp. 353-376.
7. D.A. Carlson, A. Haurie, A turnpike theory for infinite horizon open-loop competitive processes, SIAM J. Control Optim. 34 (1996) 1405-1419.
8. D.A. Carlson, Carathéodory-Hamilton-Jacobi theory for nonsmooth problems of Lagrange and optimal control, J. Math. Anal. Appl. 162 (1985) 259-273.
9. D.A. Carlson, A Carathéodory-Hamilton-Jacobi theory for infinite horizon optimal control. problems, J. Optim. Theory Appl. 48 (1986) 265-287.
10. L. Cesari, Optimization - Theory and Applications: Problems with Ordinary Differential Equations, in: Applications of Applied Mathematics, Vol. 17, Springer-Verlag, New York, 1983.
11. L.O. Courtat, Markov equilibria of stochastic games with complementarities, Games Econom. Behav. 17 (1996) 177-199.
12. A. Friedman, Differential Games, in: Pure and Applied Mathematics, Vol. XXV, John Wiley and Sons, New York, 1971.
13. A.S. Nowak, Correlated equilibria in nonzero-sum differential games, J. Math. Anal. Appl. 174 (1993) 539-549.
14. A.S. Nowak, K. Szajowski, Nonzero-sum stochastic games, in: M. Bardi, T.E.S. Raghavan, Parthasarathy (Eds.), Stochastic and Differential Games, Theory and Numerical Methods, Birkhäuser, Boston, MA, 1999, pp. 297-342.
15. D.R. Snow, Carathéodory-Hamilton-Jacobi theory in optimal control, J. Math. Anal. Appl. 16 (1967) 99-118.
16. A.W. Starr, Y.C. Ho, Nonzero-sum differential games, J. Optim. Theory Appl. 3 (1969) 184-206.
17. H. Tan, W.J. Rugh, Nonlinear overtaking optimal control: Sufficiency, stability, and approximation, IEEE Trans. Automat. Control 43 (1998) 1703-1718.
18. K. Uchida, On the existence of Nash equilibrium point in n-person nonzero-sum stochastic differential games, SIAM J. Control Optim. 16 (1978) 142-149.
19. K. Uchida, A note on the existence of Nash equilibrium point in stochastic differential games, SIAM J. Control Optim. 17 (1979) 1-4.