A d-person Differential Game with State Space Constraints by Ramasubramanian S.

By Ramasubramanian S.

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Ann. Appl. Probab. 8, 569–646 (1998) 18. : On open and closed loop bang-bang control in nonzero—sum differential games. SIAM J. Control Optim. 40, 1087–1106 (2001/2002) 342 Appl Math Optim (2007) 56: 312–342 19. : A subsidy-surplus model and the Skorokhod problem in an orthant. Math. Oper. Res. 25, 509–538 (2000) 20. : An insurance network: Nash equilibrium. Insur. Math. Econ. 38, 374–390 (2006) 21. : Open queueing networks in heavy traffic. Math. Oper. Res. 9, 441–458 (1984) 22. : Stochastic Processes for Insurance and Finance.

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. J. Optim. Theory Appl. 73, 359–385 (1992) 8. : Small BV solutions of hyperbolic noncooperative differential games. SIAM J. Control Optim. 43, 194–215 (2004) 9.

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.

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