Combinatorial Auctions with Decreasing Marginal Utilities

Title: Combinatorial Auctions with Decreasing Marginal Utilities

Abstract: This research focuses on combinatorial auctions, where multiple items are sold simultaneously and bidders express preferences about combinations of items rather than single items. The study investigates the case where bidders exhibit decreasing marginal utilities, a common assumption in microeconomic theory. The research presents algorithmic results for this case, including an efficient greedy 2-approximation algorithm. It also explores strategic aspects of combinatorial auctions with decreasing marginal utilities. The study concludes with a discussion of the implications and potential applications of these findings.

Research Question: How can combinatorial auctions be designed and managed effectively when bidders exhibit decreasing marginal utilities?

Methodology: The research employs a combination of mathematical modeling, algorithmic development, and game-theoretic analysis. It builds on existing literature and adapts techniques from various fields, including computer science, economics, and operations research. The study uses a computational approach to investigate the problem and develop solutions that are efficient and scalable.

Results: The research presents an efficient greedy 2-approximation algorithm for combinatorial auctions with decreasing marginal utilities. It also explores strategic aspects of these auctions and provides insights into bidders' behavior. The study shows that the allocation problem among bidders with decreasing marginal utilities is NP-hard, but the proposed algorithm can provide a good approximation in a reasonable amount of time.

Implications: The findings of this research have important implications for the design and management of combinatorial auctions. The algorithmic results can help auction organizers and participants to make better decisions and improve the efficiency of these auctions. The study also contributes to the broader literature on combinatorial auctions and game theory, providing new insights into the behavior of bidders and the dynamics of these markets.

Significance: Combinatorial auctions with decreasing marginal utilities are a fundamental concept in the field of auction design and game theory. This research provides a comprehensive analysis of these auctions and presents practical solutions that can be applied in real-world scenarios. The study's findings have the potential to impact various industries and markets that rely on auction-based mechanisms for allocating resources.

Link to Article: https://arxiv.org/abs/0202015v1 Authors: arXiv ID: 0202015v1