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Article Dans Une Revue Proceedings of the American Mathematical Society Année : 2020

Remarks on Nash equilibria in mean field game models with a major player

Marco Cirant
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Alessio Porretta
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Résumé

For a mean field game model with a major and infinite minor players, we characterize a notion of Nash equilibrium via a system of so-called master equations, namely a system of nonlinear transport equations in the space of measures. Then, for games with a finite number N of minor players and a major player, we prove that the solution of the corresponding Nash system converges to the solution of the system of master equations as N tends to infinity.
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Dates et versions

hal-01913985 , version 1 (06-11-2018)

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Pierre Cardaliaguet, Marco Cirant, Alessio Porretta. Remarks on Nash equilibria in mean field game models with a major player. Proceedings of the American Mathematical Society, 2020, 148 (10), pp.4241-4255. ⟨hal-01913985⟩
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