Pasting of Equilibria and Donsker-type Results for Mean Field Games

Jodi Dianetti, Max Nendel, Ludovic Tangpi and Shichun Wang
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Jodi Dianetti: Center for Mathematical Economics, Bielefeld University
Max Nendel: Center for Mathematical Economics, Bielefeld University
Ludovic Tangpi: Center for Mathematical Economics, Bielefeld University
Shichun Wang: Center for Mathematical Economics, Bielefeld University

No 743, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

Abstract: This paper studies the relation between equilibria in single-period, discrete-time and continuous-time mean field game models. First, for single-period mean field games, we establish the existence of equilibria and then prove the propagation of the Lasry-Lions monotonicity to the optimal equilibrium value, as a function of the realization of the initial condition and its distribution. Secondly, we prove a pasting property for equilibria; that is, we construct equilibria to multi-period discrete-time mean field games by recursively pasting the equilibria of suitably initialized single- period games. Then, we show that any sequence of equilibria of discrete-time mean field games with discretized noise converges (up to a subsequence) to some equilibrium of the continuous-time mean field game as the mesh size of the discretization tends to zero. When the cost functions of the game satisfy the Lasry-Lions monotonicity property, we strengthen this convergence result by providing a sharp convergence rate.

Pages: 42
Date: 2025-08-18
New Economics Papers: this item is included in nep-mic
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