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From optimal control to non-cooperative differential games: a homotopy approach. (English) Zbl 1235.91023
Summary: We propose a new approach to the study of Nash equilibrium solutions to non-cooperative differential games. The original problem is embedded in a one-parameter family of differential games, where the parameter $$\theta \in [0,1]$$ accounts for the strength of the second player. When $$\theta = 0$$, the second player adopts a myopic strategy and the game reduces to an optimal control problem for the first player. As $$\theta$$ becomes strictly positive, Nash equilibrium solutions can be obtained by studying a bifurcation problem for the corresponding system of Hamilton-Jacobi equations.

##### MSC:
 91A23 Differential games (aspects of game theory) 91A10 Noncooperative games 49N70 Differential games and control 93B52 Feedback control
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