By Ramasubramanian S.
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Additional resources for A d-person Differential Game with State Space Constraints
Oper. Res. 28, 801–835 (2003) 3. : Optimal Control and Viscosity Solutions of Hamilton-JacobiBellman Equations. Birkhauser, Boston (1997) 4. : Stochastic games for N players. J. Optim. Theory Appl. 105, 543–565 (2000) 5. : Stochastic games with risk sensitive pay offs for N players. Le Matematiche 55(Suppl. 2), 5–54 (2000) 6. : Ergodic control for constrained diffusions: characterization using HJB equations. SIAM J. Control Optim. 43, 1467–1492 (2004/2005) 7. : Stochastic differential games: occupation measure based approach.
So the only possible candidate for utopian equilibrium is (0, 0). But (0, 0) cannot be a feasible control. Hence there is no utopian equilibrium even for a single t > 0. References 1. : Singular control with state constraints on unbounded domain. Ann. Probab. 34, 1864–1909 (2006) 2. : An escape-time criterion for queueing networks: asymptotic risksensitive control via differential games. Math. Oper. Res. 28, 801–835 (2003) 3. : Optimal Control and Viscosity Solutions of Hamilton-JacobiBellman Equations.
Existence and uniqueness for a simple nonzero—sum differential game. Int. J. Game Theory 32, 33–71 (2003) 11. : Leontief systems, RBV’s and RBM’s. J. ) Proc. Imperial College workshop on Applied Stochastic Processes, pp. 1–43. Gordon and Breach, New York (1991) 12. : SDE’s with oblique reflection on nonsmooth domains. Ann. Probab. 21, 554–580 (1993) 13. : Controlled Makrov Processes and Viscosity Solutions. Springer, New York (1993) 14. : Reflected Brownian motion on an orthant. Ann. Probab. 9, 302–308 (1981) 15.