CONVERGENCE OF A PRICE PROCESS UNDER A PROBABILISTIC DOUBLE AUCTION WITH RANDOM MATCHES

买卖双方随机配对的双向拍卖价格迭代机制的收敛性研究

报告人：马金鹏 教授

报告时间：2019年6月12日星期三  下午2:30

讲座地点：东6C408学院会议室

Abstract：This paper studies a convex optimization problem that is a dual of a linear relaxation programming for a class of quasi-linear exchange economies with indivisible (or divisible) goods. Our model aims at an economy where agents' information about their own individual demands or supplies is not perfect and total demand and supply are not available for a price adjustment in search for equilibrium. We study a probabilistic  -double auction with iterations governed by a random match between buyers and sellers and are interested in the convergence of a price process it generates. We allow the weight to be a random variable with unknown distributions over [0, 1] and show a convergence result when the mean values of two random step sizes are diminishing. Then we provide conditions under which the double auction generates a price process that converges to a Walrasian equilibrium of the underlying economy with probability one. If the conditions are not satisfied, the price process may converge to a bubble or crash.

摘要：本文主要研究线性规划中的对偶凸优化问题，此类问题经常出现在准线性可分割和不可分割交换型经济中。我们主要是研究大型经济中个人信息不完全，总需求和总供给都无法获取情况下价格调整过程，研究其是否可以到达经济中的均衡点。我们研究一类随机-双向拍卖价格迭代机制。在此机制中买卖双方需要进行随机配对，而是在分布未知下可以随机在0和1间取样，两个步长也是在分布未知下随机抽取但它们的均值是随迭代步数而下降。我们指出此价格过程收敛到经济均衡点的条件。如果条件不满足，此价格过程可能会收敛到一个高于均衡水平的泡沫价格也可能收敛到一个低于均衡水平的崩溃价格。

报告人简介：Rutgers大学（罗格斯大学）-New Jersey State University 大学经济系终身教授，主要从事博弈理论，不可分割经济和双向配对方面的研究。主要贡献是有关Top Trading Cycles 机制方面的研究。

欢迎广大师生参加！

理学院

2019.06.10