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Fast Convergence in the Double Oral Auction

机译：双口腔拍卖中的快速收敛

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摘要

A classical trading experiment consists of a set of unit demand buyers and unit supply sellers with identical items. Each agent's value or opportunity cost for the item is his private information, and preferences are quasilinear. Trade between agents employs a double oral auction (DOA) in which both buyers and sellers call out bids or offers that an auctioneer recognizes. Transactions resulting from accepted bids and offers are recorded. This continues until there are no more acceptable bids or offers. Remarkably, the experiment consistently terminates in a Walrasian price. The main result of this article is a mechanism in the spirit of the DOA that converges to a Walrasian equilibrium in a polynomial number of steps, thus providing a theoretical basis for the empirical phenomenon described previously. It is well known that computation of a Walrasian equilibrium for this market corresponds to solving a maximum weight bipartite matching problem. The uncoordinated but mildly rational responses of agents thus solve in a distributed fashion a maximum weight bipartite matching problem that is encoded by their private valuations. We show, furthermore, that everyWalrasian equilibrium is reachable by some sequence of responses. This is in contrast to thewell-known auction algorithms for this problem that only allow one side to make offers and thus essentially choose an equilibrium that maximizes the surplus for the side making offers. Our results extend to the setting where not every agent pair is allowed to trade with each other.
机译：经典交易实验由一组单位需求购买者和单位供应商提供相同的物品。每个代理商的价值或机会成本是他的私人信息，偏好是准线性的。代理商之间的贸易采用了双口腔拍卖（DOA），在该拍卖中，买卖双方都呼吁拍卖师认可的出价或提供。记录由公认的投标和要约产生的交易。直到没有更多可接受的投标或报价为止。值得注意的是，该实验始终以沃尔拉斯的价格终止。本文的主要结果是DOA精神的一种机制，该机制以多项式的步骤收敛到沃尔拉斯平衡，从而为前面描述的经验现象提供了理论基础。众所周知，该市场的沃尔拉斯平衡计算对应于解决最大的重量两​​分匹配问题。因此，代理商的不协调但平均理性的反应以分布式方式解决了由其私人估值编码的最大重量双方匹配问题。此外，我们还表明，通过一系列响应可以达到每个瓦拉斯的平衡。这与此问题的知名拍卖算法相反，该算法仅允许一侧提供报价，因此从本质上选择了一个平衡，以最大程度地提高侧面制作报价的盈余。我们的结果扩展到并非每个代理对彼此交易的设置。

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