Noncooperative Games with Elliptic Systems

Noncooperative games with “slightly” nonlinear systems and “sufficiently” uniformly convex individual cost functionals may admit a relaxation having 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. The relaxation is made by a continuous extension on a suitable convex (local) compactification. This will be illustrated by semilinear elliptic systems. The regularity will be employed, too.

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