Strategic Bidding in Knapsack Auctions

Abstract

The Knapsack Problem is a well-known NP-hard problem where a set of indivisible objects, each with different values and sizes, must be packed into a fixed-size knapsack to maximize the total value. 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.

Keywords: Knapsack problem; auctions; experiment; Q-learning.

JEL Classification: D44, D82, C91, C63.