Mean Field LQ Games with a Finite Number of Agents

摘要

In this paper, we are concerned with a new class of mean field games which involve a finite number of agents. With help of conditional mathematical expectation, we obtain necessary and sufficient conditions for the existence of the decentralized open-loop Nash equilibrium for finite-population games. By decoupling a non-standard forward-backward stochastic differential equation, we design a set of decentralized strategies in term of two differential Riccati equations. Instead of the s-Nash equilibrium, the set of decentralized strategies is shown be a Nash equilibrium. Furthermore, we examine the infinite-horizon problem and give a neat condition for solvability of the related algebraic Riccati equation.