Nash Equilibria for Large-Population Linear Stochastic Systems of Weakly Coupled Agents

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Large-Population Cost-Coupled LQG Problems With Nonuniform Agents: Individual-Mass Behavior and Decentralized $\varepsilon$-Nash Equilibria (2007, background): “Propositions (3.1)–(3.3 ) may be proved by an algebraic approach [4], [14], [17].”
Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle (2006, methodology): “Our general methodology based upon state aggregation and upon individual-mass interaction was first developed for a population with linear individual dynamics or mild nonlinearity [23, 25, 28, 29, 27, 26, 30], combined with quadratic individual costs, which usually led to explicit calculations for t”
Large-Population LQG Games Involving a Major Player: The Nash Certainty Equivalence Principle (2009, methodology): “First we note that in a population solely consisting of comparably small players, each having state yi and interacting with the average state y = (1/N) ∑N i=1 yi (see [20, 21]), it has been shown that subject to self-optimizing behavior, such an averaged quantity y will collapse into a deterministic”