The object of study in the recent theory of Mean Field Games has been primarily large populations of agents interacting through a population dependent coupling term, acting either at the level of individual agent costs, and/or individual agent dynamics. However, there are situations where agents are essentially independent, except for the fact that they partially observe their own state, and the quality of their observations is affected by a population dependent interference term. This is the case for example in cellular communications where other conversations in a cell act as interference in the proper decoding of an individual's signals, and by extension situations of networked control across noisy channels. When individual control objectives are involved, this leads, albeit inadvertently, to interference induced game situations.
The case of agents described by linear stochastic dynamics with quadratic costs and partial linear observations involving the mean of all agents is considered. We investigate conditions under which the suboptimal control laws obtained by ignoring the interference term, become asymptotically optimal as the size of the agent population grows to infinity. Cooperative controls are also explored when needed. Finally, we discuss the filtering problem and the ability of growing dimension filters to help stabilize the closed loop system even when individual systems are highly unstable. Numerical results are presented.
This is joint work with Mehdi Abedinpour Fallah, Francesco Martinelli and David Saussie.