2015/05/23 by Hamidou Tembiné, Tembine, Hamidou · 3 citations
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #Computer Science and Game Theory (cs.GT) #Economic theories and models #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Multiagent Systems (cs.MA) #Optimization and Control (math.OC) #Stochastic processes and financial applications #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1505.06280
openalex publication_date 2015/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.