Continuous-Time Mean Field Games with Finite StateSpace and Common Noise

Christoph Belak, Daniel Hoffmann and Frank T. Seifried

No 2020-05, Working Paper Series from University of Trier, Research Group Quantitative Finance and Risk Analysis

Abstract: We formulate and analyze a mathematical framework for continuous-time mean field gameswith finitely many states and common noise, including a rigorous probabilistic constructionof the state process. The key insight is that we can circumvent the master equation andreduce the mean field equilibrium to a system of forward-backward systems of (random)ordinary differential equations by conditioning on common noise events. In the absenceof common noise, our setup reduces to that of Gomes, Mohr and Souza [GMS13] andCecchin and Fischer [CF20].

Keywords: mean field games; common noise; Markov chains; regime shifts (search for similar items in EconPapers)
JEL-codes: C02 (search for similar items in EconPapers)
Pages: 34 pages
Date: 2020
New Economics Papers: this item is included in nep-gth
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Persistent link: https://EconPapers.repec.org/RePEc:trr:qfrawp:202005

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