Combinatorial auctions (CAs) offer the flexibility for bidders to articulate complex preferences when competing for multiple assets. However, the behavior of bidders under different payment rules is often unclear. Our research explores the relationship between core constraints and several core-selecting payment rules. Specifically, we examine the natural and desirable property of payment rules of being , which ensures that bidding higher does not lead to lower payments. Earlier studies revealed that the VCG-nearest payment method – a commonly employed payment rule – fails to adhere to this principle even for single-minded CAs. We establish that when a exists, the payment maintains the non-decreasing property in single-minded CAs. To identify auctions where such a constraint is present, we introduce a novel framework using conflict graphs to represent single-minded CAs and establish sufficient conditions for the existence of single effective core constraints. We proceed with an analysis of the implications on bidder behavior, demonstrating that there is no overbidding in any Nash equilibrium when considering non-decreasing core-selecting payment rules. Our study concludes by establishing the non-decreasing nature of two additional payment rules, namely the proxy and proportional payment rules, for single-minded CAs.

中文翻译：

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组合拍卖中核心约束对真实出价的影响

组合拍卖 (CA) 为投标人在竞争多种资产时提供了表达复杂偏好的灵活性。然而，不同支付规则下投标人的行为往往是不明确的。我们的研究探讨了核心约束与几种核心选择支付规则之间的关系。具体来说，我们检查了支付规则的自然且理想的属性，这确保了较高的出价不会导致较低的支付。早期的研究表明，VCG 最近支付方式（一种常用的支付规则）即使对于一心一意的 CA 也未能遵守这一原则。我们确定，当 a 存在时，付款将维持单一 CA 中的非递减属性。为了识别存在此类约束的拍卖，我们引入了一种新颖的框架，使用冲突图来表示单一的 CA，并为单一有效核心约束的存在建立充分条件。我们继续分析对投标人行为的影响，证明在考虑非递减核心选择支付规则时，任何纳什均衡中都不存在过度投标。我们的研究的结论是，为一心一意的 CA 建立了两个附加支付规则的非递减性质，即代理支付规则和比例支付规则。