Natural Instability of Equilibrium Prices

Abstract

We develop a theory of market instability caused by strategic trade with complete information and without outside shocks. We focus on general equilibrium duopoly as a strategic market game with infinite strategies, and a pricing mechanism. First order conditions of the game are the 1-st kind integral equations of Fredholm, which have many solutions.

A solution is a probability distribution and can be approximated only. We suggest a modification of Tikhonov regularization for their numerical approximation. Impossibility to construct a unique and exact solution imposes a restriction on existence of converging common beliefs of players about actions of each other, on existence of rational expectations, and on price discovery property of the market, although the market is informationally efficient.

Approximated price has unremovable instabilities, 'natural instabilities', specific to parameters of a chosen approximation.

Our result is also related to existence of sun-spot equilibrium, and noise trade.

Keywords: Strategic Market Games, Ill-Posed Problems, Common Knowledge, Rational Expectations, Efficient Market, Price Fluctuations

JEL Classification: C68, C61, C72, D59, E31, E32, G14, G7