$N$-player games and mean-field games with absorption

By Luciano Campi, Markus Fischer. The Annals of Applied Probability, 2016

56 citations recorded by the source corpus.

We introduce a simple class of mean field games with absorbing boundary over a finite time horizon. In the corresponding N-player games, the evolution of players’ states is described by a system of weakly interacting Ito equations with absorption on first exit from a bounded open set. Once a player exits, her/his contribution is removed from the empirical measure of the system. Players thus interact through a renormalized empirical measure. In the definition of solution to the mean field game, the renormalization appears in form of a conditional law. We justify our definition of solution in the usual way, that is, by showing that a solution of the mean field game induces approximate Nash equilibria for the N-player games with approximation error tending to zero as N tends to infinity. This convergence is established provided the diffusion coefficient is non-degenerate. The degenerate case is more delicate and gives rise to counter-examples.

Subfields: Finance, Mathematical Physics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/861d285e76b95bad0ce3c62e6f7278ef17bb67b8

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Citations in the corpus

Mckean-Vlasov sdes with drifts discontinuous under wasserstein distance (2020, background): “This type of SDEs are also called McKean-Vlasov SDEs and mean field SDEs, and have been intensively investigated due to its wide applications, see for instance [1, 2, 5, 8, 10, 11, 12, 21, 23] and references within.”
On a strong form of propagation of chaos for McKean-Vlasov equations (2018, background): “For instance, the recent work of [4] on mean field games with absorbing states naturally gives rise to McKean-Vlasov systems with discontinuous and path-dependent coefficients.”