A Mean Field Game Approach to Equilibrium Pricing with Market Clearing Condition

Masaaki Fujii and Akihiko Takahashi
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Masaaki Fujii: Faculty of Economics, The University of Tokyo
Akihiko Takahashi: Faculty of Economics, The University of Tokyo

No CIRJE-F-1177, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

Abstract: In this work, we study an equilibrium-based continuous asset pricing problem which seeks to form a price process endogenously by requiring it to balance the ow of sale-and-purchase orders in the exchange market, where a large number of agents $1\leq i\leq N$ are interacting through the market price. Adopting a mean field game (MFG) approach, we find a special form of forward-backward stochastic differential equations of McKean-Vlasov type with common noise whose solution provides an approximate of the market price. We show the convergence of the net order flow to zero in the large N-limit and get the order of convergence in N under some conditions. An extension of the model to a setup with multiple populations, where the agents within each population share the same cost and coefficient functions but they can be different population by population, is also discussed.

Pages: 31 pages
Date: 2021-09
New Economics Papers: this item is included in nep-gth
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Persistent link: https://EconPapers.repec.org/RePEc:tky:fseres:2021cf1177

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