Bundling Equilibrium in Combinatorial Auctions

Title: Bundling Equilibrium in Combinatorial Auctions

Abstract: This research investigates the concept of bundling equilibrium in combinatorial auctions, where participants bid on bundles of goods. The study analyzes individually rational ex post equilibrium in Vickrey-Clarke (VC) combinatorial auctions, focusing on the relationship between communication complexity and economic efficiency. The authors characterize the bundling equilibrium and introduce the concept of partition-based equilibrium, where the bundles are generated by a partition. The study explores the trade-offs between communication complexity and economic efficiency, particularly in the context of partition-based equilibrium.

Main Research Question: How can we characterize the bundling equilibrium in combinatorial auctions, and what are the implications for communication complexity and economic efficiency?

Methodology: The study uses game theory and combinatorial auction design to analyze the Vickrey-Clarke (VC) combinatorial auctions. The authors focus on the ex post equilibrium, which is a situation where the participants' actions are rational given the information they have after the auction. They introduce the concept of bundling equilibrium, where the bundles of goods are selected in a way that maintains individual rationality. The study also explores the concept of partition-based equilibrium, where the bundles are generated by a partition.

Results: The study fully characterizes the bundling equilibrium in VC combinatorial auctions and introduces the concept of partition-based equilibrium. They show that the number of bundles in the equilibrium represents the communication complexity of the auction. The study also explores the trade-offs between communication complexity and economic efficiency, demonstrating that there is a limit to how efficient the auction can be without increasing the communication complexity.

Implications: The study has important implications for the design of combinatorial auctions. It provides a framework for understanding how to select bundles of goods in a way that maintains individual rationality and minimizes communication complexity. The study also highlights the trade-offs between communication complexity and economic efficiency, which is crucial for the design of practical combinatorial auction systems.

Link to Article: https://arxiv.org/abs/0201010v1 Authors: arXiv ID: 0201010v1