Consider a differential game for two players in infinite time horizon, with exponentially discounted costs. A pair of feedback controls (u * 1(x), u * 2(x))is Nash equilibrium solution if u * 1 is the best strategy for Player 1 in reply to u * 2, and u * 2 is the best strategy for Player 2, in reply to u * 1 . The aim of the present note is to investigate the stability of the best reply map: (u 1, 2→R 1(u 2)R 2(u 1)). 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 ∈ ℝ n. An example shows that stability is lost, as soon as nonlinear perturbations are considered.
All Science Journal Classification (ASJC) codes
- Applied Mathematics