Tatonnement in ongoing markets of complementary goods
Tatonnement in ongoing markets of complementary goods
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互补商品持续市场的竞争
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
Ashish Rastogi
中科院分区：
文献类型：
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作者：
Yun Kuen Cheung;R. Cole;Ashish Rastogi
本文继续了科尔和弗莱舍在[科尔和弗莱舍2008]中发起的研究，研究了正在进行的费舍尔市场中的价格更新规则的行为。先前的工作表明，快速收敛到一个均衡时，货物满足弱总替代品的属性，并有界的需求和收入弹性。
目前的工作表明，快速收敛也发生在以下类型的市场：所有对的商品是互补的，需求和收入弹性是适当的限制。
特别地，当市场中的所有购买者都配备CES效用时，这些条件成立，其中所有参数ρ，每个购买者一个，满足-1 < ρ ≤ 0。
此外，我们将上述结果推广到互补和替代混合市场。这包括表征一类快速收敛的嵌套CES实用程序。
一个有趣的技术贡献，这可能是独立的利益，是一个摊销的分析，处理异步事件的设置中，有一个连续的变化和离散事件的混合。
This paper continues the study, initiated by Cole and Fleischer in [Cole and Fleischer 2008], of the behavior of a tatonnement price update rule in Ongoing Fisher Markets. The prior work showed fast convergence toward an equilibrium when the goods satisfied the weak gross substitutes property and had bounded demand and income elasticities.
The current work shows that fast convergence also occurs for the following type of markets: All pairs of goods are complements to each other, and the demand and income elasticities are suitably bounded.
In particular, these conditions hold when all buyers in the market are equipped with CES utilities, where all the parameters ρ, one per buyer, satisfy -1 < ρ ≤ 0.
In addition, we extend the above result to markets in which a mixture of complements and substitutes occur. This includes characterizing a class of nested CES utilities for which fast convergence holds.
An interesting technical contribution, which may be of independent interest, is an amortized analysis for handling asynchronous events in settings in which there are a mix of continuous changes and discrete events.