In the Knapsack Problem a set of indivisible objects, each with different values and sizes, must be packed into a fixed-size knapsack to maximize the total value. The knapsack problem is known to be an NP-hard problem even when there is full information regarding values and sizes. In many real-world situations, however, the values of objects are private information, which adds another dimension of complexity. In this paper we examine the knapsack problem with private information by investigating three practical auctions as possible candidates for payment rules in a setup where the knapsack owner sells the space to object owners via an auction. The three auctions are the discriminatory price, the generalized second-price and the uniform-price auctions. Using a Greedy algorithm for allocating objects, we analyze bidding behavior, revenue and efficiency of these three auctions using theory, lab experiments, and AI-enriched simulations. Our results suggest that the uniform-price auction has the highest level of truthful bidding and efficiency while the discriminatory price and the generalized second-price auctions are superior in terms of revenue generation.

翻译：在背包问题中，一组不可分割的物品（每个物品具有不同的价值与尺寸）必须装入容量固定的背包中，以最大化总价值。即便在完全知晓价值与尺寸信息的情况下，背包问题也被证明是NP难问题。然而，在许多现实情境中，物品的价值属于私有信息，这增加了问题的另一层复杂性。本文通过考察三种可行的拍卖机制作为支付规则候选方案，研究存在私有信息时的背包问题，其设定为背包所有者通过拍卖向物品所有者出售空间。这三种拍卖机制分别为歧视性定价拍卖、广义第二价格拍卖和统一价格拍卖。采用贪婪算法进行物品分配后，我们结合理论分析、实验室实验及人工智能增强模拟，深入研究这三种拍卖中的投标行为、收益与效率。研究结果表明，统一价格拍卖在诚实投标与效率方面表现最优，而歧视性定价拍卖与广义第二价格拍卖则在收益生成方面更具优势。