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Strategic Bidding in Knapsack Auctions

Peyman Khezr, Vijay Mohan, Lionel Page

TL;DR

This work examines knapsack auctions where object values are private and sizes are public, embedded within a Greedy allocation framework. It analyzes three payment rules—Uniform-Price, Discriminatory Price, and Generalized Second Price—through theory, lab experiments with human bidders, and AI-driven simulations. The UP mechanism is shown to be DSIC and unique but inefficient, while DP and GSP yield higher revenue, with GSP closely matching UP in efficiency in practice. Across all methods, results indicate clear trade-offs between truthfulness, revenue, and efficiency, providing practical guidance for market design in NP-hard allocation problems under incomplete information, with AI simulations offering scalability and robustness checks.

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.

Strategic Bidding in Knapsack Auctions

TL;DR

This work examines knapsack auctions where object values are private and sizes are public, embedded within a Greedy allocation framework. It analyzes three payment rules—Uniform-Price, Discriminatory Price, and Generalized Second Price—through theory, lab experiments with human bidders, and AI-driven simulations. The UP mechanism is shown to be DSIC and unique but inefficient, while DP and GSP yield higher revenue, with GSP closely matching UP in efficiency in practice. Across all methods, results indicate clear trade-offs between truthfulness, revenue, and efficiency, providing practical guidance for market design in NP-hard allocation problems under incomplete information, with AI simulations offering scalability and robustness checks.

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.
Paper Structure (12 sections, 3 theorems, 14 equations, 16 figures, 8 tables)

This paper contains 12 sections, 3 theorems, 14 equations, 16 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Theoretical Model
  3. The Uniform-Price (UP) auction
  4. The Discriminatory Price (DP) auction
  5. The Generalized second-price (GSP) auction
  6. Experiment
  7. Experimental results
  8. Regression results
  9. AI Simulations
  10. Conclusions
  11. Appendix: Comparative statics
  12. Appendix A: Details of the experiment

Key Result

Proposition 1

The UP auction has the unique dominant-strategy incentive-compatible equilibrium of the knapsack auction game.

Figures (16)

  • Figure 1: Mean individual observations in a round.
  • Figure 2: 7 players in each auction, played for 20 rounds.
  • Figure 3: 7 players in each auction, played for 20 rounds.
  • Figure 4: 7 agents in each auction, played for 100,000 episodes.
  • Figure 5: 7 agents in each auction, played for 100,000 episodes.
  • ...and 11 more figures

Theorems & Definitions (8)

  • Proposition 1
  • proof
  • Corollary 1
  • proof
  • Remark 1
  • Proposition 2
  • proof
  • Remark 2