Abstract
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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Roubíček, T. (1999). Noncooperative Games with Elliptic Systems. In: Hoffmann, KH., Leugering, G., Tröltzsch, F., Caesar, S. (eds) Optimal Control of Partial Differential Equations. ISNM International Series of Numerical Mathematics, vol 133. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8691-8_21
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DOI: https://doi.org/10.1007/978-3-0348-8691-8_21
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