Strategic Bidding in Knapsack Auctions (2403.07928v3)
Abstract: 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.
- Aggarwal, Gagan and Jason D Hartline (2006) “Knapsack auctions,” mimeo.
- Ausubel, Lawrence M, Peter Cramton, Marek Pycia, Marzena Rostek, and Marek Weretka (2014) “Demand reduction and inefficiency in multi-unit auctions,” The Review of Economic Studies, 81 (4), 1366–1400.
- Bae, Jinsoo and John H Kagel (2019) “An experimental study of the generalized second price auction,” International Journal of Industrial Organization, 63, 44–68.
- Banchio, Martino and Andrzej Skrzypacz (2022) “Artificial intelligence and auction design,” in Proceedings of the 23rd ACM Conference on Economics and Computation, 30–31.
- Calvano, Emilio, Giacomo Calzolari, Vincenzo Denicolo, and Sergio Pastorello (2020) “Artificial intelligence, algorithmic pricing, and collusion,” American Economic Review, 110 (10), 3267–3297.
- Dantzig, George B (1957) “Discrete-variable extremum problems,” Operations research, 5 (2), 266–288.
- Edelman, Benjamin, Michael Ostrovsky, and Michael Schwarz (2007) “Internet Advertising and the Generalized Second-Price Auction: Selling Billions of Dollars Worth of Keywords,” American Economic Review, 97 (1), 242–259.
- Khezr, Peyman and Anne Cumpston (2022) “A review of multiunit auctions with homogeneous goods,” Journal of Economic Surveys, 36 (4), 1225–1247.
- Lehmann, Daniel, Liadan Ita Oćallaghan, and Yoav Shoham (2002) “Truth revelation in approximately efficient combinatorial auctions,” Journal of the ACM (JACM), 49 (5), 577–602.
- Mohan, Vijay and Peyman Khezr (2023) “MEV and the knapsack problem,” mimeo.
- Mu’Alem, Ahuva and Noam Nisan (2008) “Truthful approximation mechanisms for restricted combinatorial auctions,” Games and Economic Behavior, 64 (2), 612–631.
- Murawski, Carsten and Peter Bossaerts (2016) “How humans solve complex problems: The case of the knapsack problem,” Scientific reports, 6 (1), 34851.
- Myerson, Roger B (1981) “Optimal auction design,” Mathematics of operations research, 6 (1), 58–73.
- Nisan, Noam et al. (2007) “Introduction to mechanism design (for computer scientists),” Algorithmic game theory, 9, 209–242.
- Nisan, Noam and Amir Ronen (2007) “Computationally feasible VCG mechanisms,” Journal of Artificial Intelligence Research, 29, 19–47.
- Roughgarden, Tim (2016) Twenty lectures on algorithmic game theory: Cambridge University Press.
- Sade, Orly, Charles Schnitzlein, and Jaime F Zender (2006) “Competition and cooperation in divisible good auctions: An experimental examination,” The Review of Financial Studies, 19 (1), 195–235.