By Ramasubramanian S.
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Extra resources for A d-person Differential Game with State Space Constraints
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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.