| Abstract: |
| This work develops a general framework for two-player ergodic nonzero-sum stochastic differential games with McKean-Vlasov dynamics. A verification theorem is established, linking solutions of a system of coupled Hamilton-Jacobi-Bellman (HJB) Master equations to Nash equilibria, which are characterized via an auxiliary bias optimal control problem formulated on the space of probability measures. The paper demonstrates that the value functions of this auxiliary control problem are uniquely determined, up to an additive constant, by the uniqueness of the invariant measure associated with the optimally controlled state process. The framework is further illustrated in a Linear-Quadratic-Gaussian (LQG) setting, where explicit solutions to the Master equations are obtained by exploiting their polynomial structure in the measure variables. |
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