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arXiv · 2302.10689

Differential N-players game: Nash equilibria and Mather measures

Cristian Mendico
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Abstract

We study Nash equilibria for the deterministic ergodic N-players game. We introduce pure strategies, mixed strategies and Nash equilibria associated with those. We show that a Nash equilibrium in mixed strategies exists and it is a Mather measure for the Lagrangian system defined by the cost functional. In conclusion, we show that the mean field limit of the N-players game is described by the ergodic PDE's system for a continuum of players.

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Cristian Mendico. 2023-02-21. Differential N-players game: Nash equilibria and Mather measures. https://doi.org/10.1093/imamci%2Fdnad006

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