Discrete-time linear-quadratic mean-field-type repeated games: Perfect, incomplete, and imperfect information

In this paper, we study linear-quadratic mean-field-type repeated games with arbitrary number of interacting decision-makers. Different information structures are examined: (i) perfect knowledge of the model, (ii) imperfect knowledge of the model; under perfect state observation. We provide semi-explicit solutions for both non-cooperative and cooperative cases. The state dynamics is given by a stochastic difference equation that includes mean-field terms, i.e., the expected value for both the state and control inputs. In addition, the cost function incorporates, not only the expected value of the states, but also the variance of both system state and control inputs. The effect of the information is quantified using price of anarchy and price of imperfect information. Finally, some numerical examples are presented.