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摘要翻译：
虽然拍卖理论认为出价和估价是连续变量，但现实世界的拍卖必然是离散的。在本文中，我们使用分析和计算相结合的方法来研究引入离散性是否会实质性地改变拍卖理论的预测，重点是在一致分布的估价情况下，以便我们的结果适用于大多数拍卖实验。在某些情况下，我们发现引入离散性变化不大。例如，有两个出价人和偶数个值的第一价格拍卖具有一个对称均衡，该均衡与连续对应物非常相似，并随着离散度趋于零时收敛到连续对应物。然而，在其他情况下，我们发现了不连续的结果。例如，在全薪拍卖中引入任意少量的离散性，使其对称的纯策略均衡消失；并出现（基于计算实验）完全抢夺纯策略均衡的博弈。这些结果对拍卖理论所基于的连续性近似提出了质疑，并促使对实验文献的重新评价。
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英文标题：
《The importance of being discrete: on the inaccuracy of continuous
approximations in auction theory》
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作者：
Itzhak Rasooly and Carlos Gavidia-Calderon
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最新提交年份：
2021
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分类信息：
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：
While auction theory views bids and valuations as continuous variables, real-world auctions are necessarily discrete. In this paper, we use a combination of analytical and computational methods to investigate whether incorporating discreteness substantially changes the predictions of auction theory, focusing on the case of uniformly distributed valuations so that our results bear on the majority of auction experiments. In some cases, we find that introducing discreteness changes little. For example, the first-price auction with two bidders and an even number of values has a symmetric equilibrium that closely resembles its continuous counterpart and converges to its continuous counterpart as the discretisation goes to zero. In others, however, we uncover discontinuity results. For instance, introducing an arbitrarily small amount of discreteness into the all-pay auction makes its symmetric, pure-strategy equilibrium disappear; and appears (based on computational experiments) to rob the game of pure-strategy equilibria altogether. These results raise questions about the continuity approximations on which auction theory is based and prompt a re-evaluation of the experimental literature.
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PDF链接：
https://arxiv.org/pdf/2006.03016
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