This paper examines knapsack auctions as a method to solve the knapsack problem with incomplete information, where object values are private and sizes are public. We analyze three auction types-uniform price (UP), discriminatory price (DP), and generalized second price (GSP)-to determine efficient resource allocation in these settings. 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. This study not only deepens the understanding of auction-based approaches to NP-hard problems but also provides practical insights for market design.

翻译：本文探讨了背包拍卖作为在信息不完全情况下解决背包问题的一种方法，其中物品价值为私有信息，而尺寸为公共信息。我们分析了三种拍卖类型——统一价格拍卖、歧视性价格拍卖和广义第二价格拍卖——以确定在这些情境下的高效资源配置。通过采用贪心算法来分配物品，我们结合理论、实验室实验以及人工智能增强的模拟，分析了这三种拍卖的投标行为、收益和效率。我们的研究结果表明，统一价格拍卖在真实投标和效率方面表现最佳，而歧视性价格拍卖和广义第二价格拍卖在收益产生方面更具优势。本研究不仅加深了对基于拍卖的NP难问题解决方案的理解，还为市场设计提供了实践洞察。