论文标题
离散的重要性：在拍卖理论中连续近似的不准确性
The importance of being discrete: on the inaccuracy of continuous approximations in auction theory
论文作者
论文摘要
尽管拍卖理论将投标和估值视为连续变量，但实际拍卖必然是离散的。在本文中，我们使用分析方法和计算方法的组合来研究合并离散性是否会实质性地改变拍卖理论的预测，重点是均匀分布的估值，以使我们的结果依赖于大多数拍卖实验。在某些情况下，我们发现引入离散性的变化很小。例如，带有两个投标人和偶数值的第一价格拍卖具有对称平衡，它与其连续的对应物非常相似，并且随着离散化为零而收敛到其连续的对应物。但是，在其他情况下，我们发现了不连续性结果。例如，将任意少量的离散性引入全付拍卖会使其对称，纯净的平衡消失。并出现（基于计算实验），以完全抢劫纯净的平衡游戏。这些结果提出了有关拍卖理论所基于的连续性近似的问题，并促使对实验文献进行重新评估。
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.
