Auction is applied for trade with various mechanisms. A simple but practical question is which mechanism, typically first-price or second-price auctions, is preferred from the perspective of bidders or sellers. A celebrated answer is revenue equivalence, where each bidder's equilibrium payoff is proven to be independent of auction mechanisms (and a seller's revenue, too). In reality, however, auction environments like the value distribution of items would vary over time, and such equilibrium bidding cannot always be achieved. Indeed, bidders must continue to track their equilibrium bidding by learning in first-price auctions, but they can keep their equilibrium bidding in second-price auctions. This study discusses whether and how revenue equivalence is violated in the long run by comparing the time series of non-equilibrium bidding in first-price auctions with those of equilibrium bidding in second-price auctions. We characterize the value distribution by two parameters: its basis value, which means the lowest price to bid, and its value interval, which means the width of possible values. Surprisingly, our theorems and experiments find that revenue equivalence is broken by the correlation between the basis value and the value interval, uncovering a novel phenomenon that could occur in the real world.

翻译：拍卖被应用于多种交易机制中。一个简单而实际的问题是，从投标人或卖方的角度来看，通常首选哪种机制——是第一价格拍卖还是第二价格拍卖。一个著名的答案是收益等价定理，该定理证明每个投标人的均衡收益与拍卖机制无关（卖方的收益亦如此）。然而在现实中，拍卖环境（如物品的价值分布）会随时间变化，这种均衡出价并不总能实现。事实上，在第一价格拍卖中，投标人必须通过学习持续追踪其均衡出价策略，而在第二价格拍卖中，他们则可以保持均衡出价。本研究通过比较第一价格拍卖中非均衡出价的时间序列与第二价格拍卖中均衡出价的时间序列，探讨了收益等价定理在长期中是否以及如何被违反。我们通过两个参数来刻画价值分布：其基础价值（即投标的最低价格）和价值区间（即可能价值的宽度）。令人惊讶的是，我们的定理和实验发现，收益等价定理被基础价值与价值区间之间的相关性所打破，这揭示了一种在现实世界中可能发生的新现象。