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On noncooperative nonlinear differential games. (English) Zbl 1274.91073
Summary: Noncooperative games with systems governed by nonlinear differential equations remain, in general, nonconvex even if continuously extended (i.e., relaxed) in terms of Young measures. However, if the individual payoff functionals are “enough” uniformly convex and the controlled system is only “slightly” nonlinear, then the relaxed game enjoys a globally convex structure, which guarantees existence of its Nash equilibria as well as existence of approximate Nash equilibria (in a suitable sense) for the original game.

MSC:
91A23 Differential games (aspects of game theory)
91A10 Noncooperative games
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