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Linear Quadratic Nash Systems and Master Equations in Hilbert Spaces
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This paper aims to develop a theory for linear-quadratic Nash systems and Master equations in possibly infinite-dimensional Hilbert spaces. As a first step and motivated by the recent results in [31], we study a more general model in the linear quadratic case where the dependence on the distribution enters just in the objective functional through the mean. This property enables the Nash systems and the Master equation to be reduced to two systems of coupled Riccati equations and backward abstract evolution equations. We show that solutions for such systems exist and are unique for all time horizons, a result that is completely new in the literature in our setting. Finally, we apply the results to a vintage capital model, where capital depends on time and age, and the production function depends on the mean of the vintage capital.
Forward citations
Cited by 2 Pith papers
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Infinite-Dimensional LQ Mean Field Games with Common Noise: Small and Arbitrary Finite Time Horizons
Infinite-dimensional linear-quadratic mean field games with common noise have unique equilibria for small time horizons and, under deterministic common-noise diffusion, for arbitrary finite time horizons.
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Linear-quadratic stochastic nonzero-sum differential games between graphon teams
For a linear-quadratic nonzero-sum game between two graphon teams, the paper derives a Nash equilibrium from coupled Riccati equations and proves existence for sufficiently small cross-team coupling.
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