Risk-sensitive mean-field-type games with LpLp-norm drifts
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Hamidou Tembine [1]
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[1] University Abu Dhabi, United Arab Emirates
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- Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Vol. 59, 2015, págs. 224-237
- Idioma: inglés
- Texto completo no disponible (Saber más ...)
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Resumen
We study how risk-sensitive players act in situations where the outcome is influenced not only by the state–action profile but also by the distribution of it. In such interactive decision-making problems, the classical mean-field game framework does not apply. We depart from most of the mean-field games literature by presuming that a decision-maker may include its own-state distribution in its decision. This leads to the class of mean-field-type games. In mean-field-type situations, a single decision-maker may have a big impact on the mean-field terms for which new type of optimality equations are derived. We establish a finite dimensional stochastic maximum principle for mean-field-type games where the drift functions have a pp-norm structure which weaken the classical Lipschitz and differentiability assumptions. Sufficient optimality equations are established via Dynamic Programming Principle but in infinite dimension. Using de Finetti–Hewitt–Savage theorem, we show that a propagation of chaos property with virtual particles holds for the non-linear McKean–Vlasov dynamics.
