Title :
ε-Nash equilibria for a partially observed mean field game with major player
Author :
Sen, Nevroz ; Caines, Peter E.
Author_Institution :
Dept. of Electr. & Comput. Eng., McGill Univ., Montreal, QC, Canada
Abstract :
Consider a dynamic game with a population of N minor agents, where N is very large, and a major agent where the agents are coupled in their nonlinear dynamics and cost functions such that even asymptotically as the population size goes to infinity the major agent has a non-vanishing effect on the minor agents. Such games are referred to as mean field games with major-minor agents (MM-MFG) and for MM-MFG, it has been demonstrated the mean field term is stochastic and the best response control actions of the minor agents depend on the state of the major agent as well as this stochastic mean field. In practical applications one is led to consider the situation where the minor agents partially observe (PO) the state of the major agent. In this work, we consider a restricted case of this scenario and demonstrate that in the case the minor agents are coupled to the major agent only through their cost functions, one can obtain the ε-Nash equilibrium property for the PO-MM-MFG best response control actions as the population size N goes to infinity.
Keywords :
stochastic games; ε-Nash equilibrium property; PO-MM-MFG best response control; cost functions; dynamic game; major player; major-minor agents; nonlinear dynamics; nonvanishing effect; partially-observed mean field game; population size; stochastic mean field term; Cost function; Games; Mathematical model; Process control; Sociology; Standards; Statistics;
Conference_Titel :
American Control Conference (ACC), 2015
Conference_Location :
Chicago, IL
Print_ISBN :
978-1-4799-8685-9
DOI :
10.1109/ACC.2015.7172084