# Price Convergence under a Probabilistic Double Auction

Xiaojing Xu (), Jinpeng Ma () and Xiaoping Xie ()
Xiaojing Xu: Southwest University of Science and Technology
Jinpeng Ma: Rutgers University
Xiaoping Xie: Sichuan University

Computational Economics, 2019, vol. 54, issue 3, 1113-1155

Abstract: 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 $$\alpha$$ α -double auction and are interested in the convergence of a price process it generates, with weight $$\alpha$$ α 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 $$\alpha$$ α 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.

Keywords: Probabilistic double auctions; Incremental subgradient methods; Walrasian equilibrium; Indivisible objects (search for similar items in EconPapers)
JEL-codes: C42 C44 C72 D63 (search for similar items in EconPapers)
Date: 2019
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