In auctions with externalities, it is well‐known that the core can be empty, which is undesirable both in terms of stability and “fairness.” Nevertheless, some auction outcome must be chosen. We separate deviations into two types: deviations by paying more and deviations by refusing to pay. In high‐stakes auctions where bidders also care about their reputation, the latter are unlikely to occur, or else can be prevented by legal interventions. In contrast, the former is more undesirable in the sense that the seller and the bidders experience justified envy. We show that the core is nonempty if bidders cannot refuse to pay.

中文翻译：

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具有外部性的拍卖的核心：稳定与公平

在具有外部性的拍卖中，众所周知，核心可以是空的，这在稳定性和“公平性”方面都是不可取的。但是，必须选择一些拍卖结果。我们将偏差分为两种：通过支付更多的偏差和通过拒绝支付的偏差。在竞标者也关心其声誉的高风险拍卖中，后者不太可能发生，或者可以通过法律干预来阻止。相反，从卖方和投标人都感到正当的嫉妒的意义上讲，前者是更不可取的。我们证明，如果投标人无法拒绝付款，则核心是非空的。