A d-person differential game with state space constraints

Applied Mathematics and Optimization

Volumn 56, Issue 3, 2007, Pages 312-342

  Ramasubramanian, S ^a  

^a INDIAN STATISTICAL INSTITUTE   (India)

Author keywords

Constrained viscosity solution; D person differential game; Deterministic Skorokhod problem; Drift; Dynamic programming principle; Nash equilibrium; Reflection; Semicontinuous envelope; State space constraints; System of HJB equations; Utopian equilibrium

Indexed keywords

DIFFERENTIAL GAME; NASH EQUILIBRIUM; STATE SPACE CONSTRAINTS; UTOPIAN EQUILIBRIUM;

BOUNDARY CONDITIONS; COSTS; HAMILTONIANS; PROBLEM SOLVING; PRODUCT LIABILITY; VISCOSITY;

STATE SPACE METHODS;

EID: 36749012915     PISSN: 00954616     EISSN: 14320606     Source Type: Journal    
DOI: 10.1007/s00245-007-9011-z     Document Type: Article

References (24)

1. Atar, R., Budhiraja, A.: Singular control with state constraints on unbounded domain. Ann. Probab. 34, 1864-1909 (2006)
2. Atar, R., Dupuis, P., Shwartz, A.: An escape-time criterion for queueing networks: asymptotic risk-sensitive control via differential games. Math. Oper. Res. 28, 801-835 (2003)
3. Bardi, M., Capuzzo-Dolcetta, I.: Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations. Birkhauser, Boston (1997)
4. Bensoussan, A., Frehse, J.: Stochastic games for N players. J. Optim. Theory Appl. 105, 543-565 (2000)
5. Bensoussan, A., Frehse, J.: Stochastic games with risk sensitive pay offs for N players. Le Matematiche 55(Suppl. 2), 5-54 (2000)
6. Borkar, V.S., Budhiraja, A.: Ergodic control for constrained diffusions: characterization using HJB equations. SIAM J. Control Optim. 43, 1467-1492 (2004/2005)
7. Borkar, V.S., Ghosh, M.K.: Stochastic differential games: occupation measure based approach. J. Optim. Theory Appl. 73, 359-385 (1992)
8. Bressan, A., Shen, W.: Small BV solutions of hyperbolic noncooperative differential games. SIAM J. Control Optim. 43, 194-215 (2004)
9. Capuzzo-Dolcetta, I., Lions, P.-L.: Hamilton-Jacobi equations with state constraints. Trans. A.M.S. 318, 643-683 (1990)
10. Cardaliaguet, P., Plaskacz, S.: Existence and uniqueness for a simple nonzero-sum differential game. Int. J. Game Theory 32, 33-71 (2003)
11. Chen, H., Mandelbaum, A.: Leontief systems, RBV's and RBM's. In: Davis, M.H.A., Elliott, R.J. (eds.) Proc. Imperial College workshop on Applied Stochastic Processes, pp. 1-43. Gordon and Breach, New York (1991)
12. Dupuis, P., Ishii, H.: SDE's with oblique reflection on nonsmooth domains. Ann. Probab. 21, 554-580 (1993)
13. Fleming, W., Soner, H.: Controlled Makrov Processes and Viscosity Solutions. Springer, New York (1993)
14. Harrison, J.M., Reiman, M.I.: Reflected Brownian motion on an orthant. Ann. Probab. 9, 302-308 (1981)
15. Leitmann, G.: Cooperative and Non-Cooperative Many Players Differential Games. Springer, Wien (1974)
16. Manucci, P.: Nonzero sum stochastic differential games with discontinuous feedback. SIAM J. Control Optim. 43, 1222-1233 (2004/2005)
17. Mandelbaum, A., Pats, G.: State-dependent stochastic networks. Part I: approximations and applications with continuous diffusion limits. Ann. Appl. Probab. 8, 569-646 (1998)
18. Olsder, G.J.: On open and closed loop bang-bang control in nonzero-sum differential games. SIAM J. Control Optim. 40, 1087-1106 (2001/2002)
19. Ramasubramanian, S.: A subsidy-surplus model and the Skorokhod problem in an orthant. Math. Oper. Res. 25, 509-538 (2000)
20. Ramasubramanian, S.: An insurance network: Nash equilibrium. Insur. Math. Econ. 38, 374-390 (2006)
21. Reiman, M.I.: Open queueing networks in heavy traffic. Math. Oper. Res. 9, 441-458 (1984)
22. Rolski, T., Schmidli, H., Schmidt, V., Teugels, J.: Stochastic Processes for Insurance and Finance. Wiley, New York (2001)
23. Shashiashvili, M.: A lemma of variational distance between maximal functions with application to the Skorokhod problem in a nonnegative orthant with state dependent reflection directions. Stoch. Stoch. Rep. 48, 161-194 (1994)
24. Soner, H.M.: Optimal control with state space constraints I. SIAM J. Control Optim. 24, 552-561 (1986)