ON THE STABILITY OF THE BEST REPLY MAP FOR NONCOOPERATIVE DIFFERENTIAL GAMES
2012 ◽
Vol 10
(02)
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pp. 113-132
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Keyword(s):
Consider a differential game for two players in infinite time horizon, with exponentially discounted costs. A pair of feedback controls [Formula: see text] is Nash equilibrium solution if [Formula: see text] is the best strategy for Player 1 in reply to [Formula: see text], and [Formula: see text] is the best strategy for Player 2, in reply to [Formula: see text]. The aim of the present note is to investigate the stability of the best reply map: [Formula: see text]. For linear-quadratic games, we derive a condition which yields asymptotic stability, within the class of feedbacks which are affine functions of the state x ∈ ℝn. An example shows that stability is lost, as soon as nonlinear perturbations are considered.
1977 ◽
Vol 22
(3)
◽
pp. 490-491
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1976 ◽
Vol 21
(4)
◽
pp. 547-550
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1996 ◽
Vol 29
(3)
◽
pp. 121-129
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1982 ◽
Vol 104
(1)
◽
pp. 27-32
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Keyword(s):
2021 ◽
Vol 12
(1)
◽
pp. 77-97