On Equilibrium Existence in a Finite-Agent, Multi-Asset Noisy Rational Expectations Economy

Carpio Ronaldo () and Guo Meixin ()
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Carpio Ronaldo: School of Banking and Finance, University of International Business and Economics, 913 Boxue Bldg, 10 Huixindongjie, Chaoyang District, Beijing, 100029, China
Guo Meixin: School of Economics and Management, Tsinghua University, Beijing, 100084, China

The B.E. Journal of Theoretical Economics, 2020, vol. 20, issue 1, 17

Abstract: We introduce a novel method of proving existence of rational expectations equilibria (REE) in multi-dimensional CARA-Gaussian environments. Our approach is to construct a mapping from agents’ initial beliefs (which are characterized by a positive semidefinite matrix), to their updated beliefs, after reaching and observing equilibrium; we then show Brouwer’s fixed point theorem applies. We apply our approach to a finite-market version of Admati (1985), which is a multi-asset noisy REE asset pricing model with dispersed information. We present an algorithm to numerically solve for equilibrium of the finite model, as well as several examples illustrating the difference in equilibrium behavior between the finite and infinite models. Our method can be applied to any multi-dimensional REE model with Gaussian uncertainty and behavior that is linear in agents’ information.

Keywords: asymmetric information; noisy rational expectations; equilibrium existence (search for similar items in EconPapers)
JEL-codes: C62 G12 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1515/bejte-2018-0144

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