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By Ramasubramanian S.

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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.

Appl Math Optim (2007) 56: 312–342 341 Solution to the corresponding Skorokhod problem is given by Y1 (t) ≡ 0, Y2 (t) = t, Z1 (t) = (1 + R12 )t, Z2 (t) ≡ 0. 4 the solution to the Skorokhod problem gives a Nash equilibrium; this also follows from the argument given below. Let λ1 ≥ 0, 0 ≤ λ2 ≤ 1 be such that λ2 + R21 λ1 = 1. Put yˆ1 (t) = λ1 (t), yˆ2 (t) = λ2 t. Fix yˆ1 (·). Let 0 ≤ y2 (t) < λ2 t for some t. Corresponding to yˆ1 (·), y2 (·) note that z1 (t) ≥ 0 but z2 (t) = −t + y2 (t) + R21 yˆ1 (t) < 0.

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. : Hamilton-Jacobi equations with state constraints. Trans. S. 318, 643–683 (1990) 10. : 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.

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


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