Long-Run Behavior and Convergence of Dynamic Mean Field Equilibria

Christoph Knochenhauer () and Berenice Anne Neumann ()
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Christoph Knochenhauer: Technical University of Munich
Berenice Anne Neumann: Trier University

Dynamic Games and Applications, 2025, vol. 15, issue 5, No 6, 1646-1684

Abstract: Abstract We study the behavior of dynamic equilibria in mean field games with large time horizons in a dynamic consumer choice model. We show that if the stationary equilibrium in the associated infinite horizon game is unique, the dynamic equilibria of the finite horizon games converge to the stationary equilibrium of the infinite horizon game as the time horizon tends to infinity. If the stationary equilibrium is not unique, however, the situation becomes more involved. In this case, we show that in addition to convergence to the stationary equilibria, in the long run, the dynamic equilibria circle around randomized stationary equilibria for certain choices of boundary data.

Keywords: Mean field game; Dynamic equilibrium; Stationary equilibrium; Turnpike property (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13235-024-00604-4

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