Stochastic LQ Games Involving A Major Player And A Large Number Of Minor Players

The paper discusses stochastic linear quadratic games involving a major player and a large number of minor players.The major player has significant influence on others.The minor players individually have negligible impact,but they collectively contribute mean field coupling terms in the individual dynamics and costs.Both finite and infinite time-horizon stochastic linear quadratic games are considered in the paper. NCE(Nash certainty equivalence) equations are derived,closed-loop behavior of agents is analyzed,andε-Nash equilibria are given in both cases.The results of the paper generalize the existing ones by considering the appearance of the state and control in the diffusion term.