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arXiv · 1505.06280

Risk-Sensitive Mean-Field-Type Games with Lp-norm Drifts

Hamidou Tembine
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Abstract

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 p-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.

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Hamidou Tembine. 2015-05-23. Risk-Sensitive Mean-Field-Type Games with Lp-norm Drifts. https://arxiv.org/abs/1505.06280

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