Competitive Rational Expectations Equilibria without Apology

Abstract

In a standard financial market model with asymmetric information with a finite number N of risk-averse informed traders, competitive rational expectations equilibria provide a good approximation to strategic equilibria as long as N is not too small: equilibrium prices in each situation converge to each other at a rate of 1/N as the market becomes large. The approximation is particularly good when the informationally adjusted risk bearing capacity of traders is not very large. This is not the case if informed traders are close to risk neutral. Both equilibria converge to the competitive equilibrium of an idealized limit continuum economy as the market becomes large at a slower rate of 1/(square root of N) and, therefore, the limit equilibrium need not be a good approximation of the strategic equilibrium in moderately large markets.

Keywords: 'schizophrenia' problem, strategic equilibrium, large markets, information acquisition, free entry, rate of convergence

JEL Classification: C22, G10, G12, D41, D43