On the Solvability of Risk-Sensitive Linear-Quadratic Mean-Field Games

摘要: In this paper we formulate and solve a mean-field game described by linear stochastic dynamics quadratic or exponential-quadratic cost functional for each generic player. The optimal strategies the players are given explicitly using simple direct method based on square completion Girsanov-type change of measure. This approach does not use well-known solution methods such as Stochastic Maximum Principle Dynamic Programming with Hamilton-Jacobi-Bellman-Isaacs equation Fokker-Planck-Kolmogorov equation. risk-neutral linear-quadratic game, show that there is unique best response strategy to mean state provide sufficient condition existence uniqueness equilibrium. gives basic insight into providing explanation additional term in robust risk-sensitive Riccati equation, compared Sufficient conditions equilibria obtained when horizon length risk-sensitivity index small enough. then extended games under disturbance, formulated minimax game.