Price Convergence under a Probabilistic Double Auction

Abstract

This paper uses a dual approach to study a class of quasi-linear exchange economies with indivisible or divisible goods in search for an equilibrium. Our model aims at an economy with a large scale and an agent’s individual demand or supply is contaminated with stochastic errors (noises). We study a probabilistic $$\alpha $$ -double auction and are interested in the convergence of a price process it generates, with weight $$\alpha $$ being a random variable with unknown distributions over [0, 1]. We show convergence results when the two step sizes are diminishing or probabilistically diminishing in the means. An error bound is estimated when the two step sizes are constant, bounded away from zero, while $$\alpha $$ remains a random variable. We provide conditions under which the double auction generates a price process that converges in mean square to the set of Walrasian equilibrium prices of the underlying economy.