Deviation from Bilateral Equilibrium in a Random Exchange Market

A model of Edgeworthian economies is studied, where at each time period, the participants are randomly matched in pairs to exchange two goods with the aim of increasing their utilities, given by Cobb-Douglas utility functions. They are allowed to trade in deviation from their bilateral equilibrium, provided that the market and the trade follow appropriate symmetry conditions. It is shown that at each time period, the expectation of the logarithm of the trading price is equal to the expectation of the logarithm of the Walrasian price, being both fixed along time