摘要翻译：
我们研究交换经济中的比例反应动态，其中每个参与者都从一定数量的钱和一个好的开始。每天，玩家带上一个单位的商品，对他们喜欢的商品进行投标，每件商品按投标金额的比例分配，每个卖家收集收到的投标。然后，每个玩家更新出价的比例，以贡献的每一个商品在他们的效用。这个动态模型是一个学习如何投标的过程，在一系列关于费舍尔市场和生产市场的论文中已经研究过，但在交换经济中没有研究过。我们的主要结果如下：-对于线性公用事业，动态收敛于市场均衡公用事业和分配，而出价和价格可能是循环的。给出了价格和投标极限环的组合刻画。-我们引入了一个懒惰的动态版本，玩家可以为以后省钱，并显示这在一切方面都是一致的：公用事业，分配和价格。-对于替代范围为$[0,1)$的CES效用，所有参数的动态收敛。这回答了一个关于线性效用的交换经济的公开问题，其中tatonnement不收敛于市场均衡，也不知道导致均衡的自然过程。我们还注意到，比例响应是一个参与者在整个时间内交换商品的过程（在非均衡状态下），而tatonnement只解释了在极限情况下交换是如何发生的。
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英文标题：
《Proportional Dynamics in Exchange Economies》
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作者：
Simina Br\^anzei and Nikhil R. Devanur and Yuval Rabani
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最新提交年份：
2019
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分类信息：

一级分类：Computer Science        计算机科学
二级分类：Computer Science and Game Theory        计算机科学与博弈论
分类描述：Covers all theoretical and applied aspects at the intersection of computer science and game theory, including work in mechanism design, learning in games (which may overlap with Learning), foundations of agent modeling in games (which may overlap with Multiagent systems), coordination, specification and formal methods for non-cooperative computational environments. The area also deals with applications of game theory to areas such as electronic commerce.
涵盖计算机科学和博弈论交叉的所有理论和应用方面，包括机制设计的工作，游戏中的学习（可能与学习重叠），游戏中的agent建模的基础（可能与多agent系统重叠），非合作计算环境的协调、规范和形式化方法。该领域还涉及博弈论在电子商务等领域的应用。
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一级分类：Economics        经济学
二级分类：Theoretical Economics        理论经济学
分类描述：Includes theoretical contributions to Contract Theory, Decision Theory, Game Theory, General Equilibrium, Growth, Learning and Evolution, Macroeconomics, Market and Mechanism Design, and Social Choice.
包括对契约理论、决策理论、博弈论、一般均衡、增长、学习与进化、宏观经济学、市场与机制设计、社会选择的理论贡献。
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英文摘要：
  We study the Proportional Response dynamic in exchange economies, where each player starts with some amount of money and a good. Every day, the players bring one unit of their good and submit bids on goods they like, each good gets allocated in proportion to the bid amounts, and each seller collects the bids received. Then every player updates the bids proportionally to the contribution of each good in their utility. This dynamic models a process of learning how to bid and has been studied in a series of papers on Fisher and production markets, but not in exchange economies. Our main results are as follows:   - For linear utilities, the dynamic converges to market equilibrium utilities and allocations, while the bids and prices may cycle. We give a combinatorial characterization of limit cycles for prices and bids.   - We introduce a lazy version of the dynamic, where players may save money for later, and show this converges in everything: utilities, allocations, and prices.   - For CES utilities in the substitute range $[0,1)$, the dynamic converges for all parameters.   This answers an open question about exchange economies with linear utilities, where tatonnement does not converge to market equilibria, and no natural process leading to equilibria was known. We also note that proportional response is a process where the players exchange goods throughout time (in out-of-equilibrium states), while tatonnement only explains how exchange happens in the limit.
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PDF链接：
https://arxiv.org/pdf/1907.05037