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Counteracting Inequality in Markets via Convex Pricing
arXiv - CS - Computer Science and Game Theory Pub Date : 2020-09-20 , DOI: arxiv-2009.09351
Ashish Goel and Benjamin Plaut

We study market mechanisms for allocating divisible goods to competing agents with quasilinear utilities. For \emph{linear} pricing (i.e., the cost of a good is proportional to the quantity purchased), the First Welfare Theorem states that Walrasian equilibria maximize the sum of agent valuations. This ensures efficiency, but can lead to extreme inequality across individuals. Many real-world markets -- especially for water -- use \emph{convex} pricing instead, often known as increasing block tariffs (IBTs). IBTs are thought to promote equality, but there is a dearth of theoretical support for this claim. In this paper, we study a simple convex pricing rule and show that the resulting equilibria are guaranteed to maximize a CES welfare function. Furthermore, a parameter of the pricing rule directly determines which CES welfare function is implemented; by tweaking this parameter, the social planner can precisely control the tradeoff between equality and efficiency. Our result holds for any valuations that are homogeneous, differentiable, and concave. We also give an iterative algorithm for computing these pricing rules, derive a truthful mechanism for the case of a single good, and discuss Sybil attacks.

中文翻译:

通过凸定价抵消市场不平等

我们研究了将可分割的商品分配给具有拟线性效用的竞争代理的市场机制。对于 \emph{linear} 定价(即,商品的成本与购买的数量成正比),第一福利定理指出瓦尔拉斯均衡最大化代理估值的总和。这确保了效率,但可能导致个人之间的极端不平等。许多现实世界的市场——尤其是水——使用\emph{凸}定价,通常被称为增加块关税(IBT)。IBT 被认为可以促进平等,但这种说法缺乏理论支持。在本文中,我们研究了一个简单的凸定价规则,并表明由此产生的均衡可以保证最大化 CES 福利函数。此外,定价规则的一个参数直接决定了执行哪个CES福利函数;通过调整这个参数,社会规划者可以精确地控制平等和效率之间的权衡。我们的结果适用于任何同质、可微和凹的估值。我们还给出了计算这些定价规则的迭代算法,推导出单一商品情况下的真实机制,并讨论女巫攻击。
更新日期:2020-09-22
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