Risk-Sensitive Linear-Quadratic Mean-Field Games:Asymptotic Solvability and Decentralized O(1/N)-Nash Equilibria In honour of the 80th birthday of Professor Peter Caines

This paper considers risk-sensitive linear-quadratic mean-field games. By the so-called direct approach via dynamic programming, the authors determine the feedback Nash equilibrium in an N-player game. Subsequently, the authors design a set of decentralized strategies by passing to the mean-field limit. The authors prove that the set of decentralized strategies constitutes an O(1/N)-Nash equilibrium when applied by the N players, and hence obtain so far the tightest equilibrium error bounds for this class of models.