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By Ramasubramanian S.

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Extra resources for A d-person Differential Game with State Space Constraints

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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. : Optimal control with state space constraints I. SIAM J. Control Optim.

Ann. Probab. 9, 302–308 (1981) 15. : Cooperative and Non-Cooperative Many Players Differential Games. Springer, Wien (1974) 16. : Nonzero sum stochastic differential games with discontinuous feedback. SIAM J. Control Optim. 43, 1222–1233 (2004/2005) 17. : State-dependent stochastic networks. Part I: approximations and applications with continuous diffusion limits. 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.

In an entirely analogous manner with yˆ2 (·) fixed, y1 (·) cannot be feasible unless y1 (t) ≥ λ1 t for all t. Therefore it follows that for any λ1 , λ2 as above (uˆ 1 (·), uˆ 2 (·)) ≡ (λ1 , λ2 ) gives a Nash equilibrium for each t ≥ 0. So even Nash equilibrium serving for all t need not be unique. Next note that (λ1 , λ2 ) = (0, 1) as well as (λ1 , λ2 ) = ( R121 , 0) give feasible controls (in fact both are Nash equilibria). So the only possible candidate for utopian equilibrium is (0, 0). But (0, 0) cannot be a feasible control.

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