An efficiency ordering of k-price auctions under complete information

2025-07-08

AI Summary

This paper investigates the social efficiency ranking of k-price auctions (k = 2, …, n) under complete information, focusing on n agents with ordered valuations. Using a non-cooperative game-theoretic model and analyzing pure-strategy Nash equilibria, we fully characterize the equilibrium outcomes: any agent except the k−2 lowest-valued ones may win. Our key contribution is establishing, for the first time, the monotonicity of worst-case social welfare in k-price auctions—specifically, as k increases from 2 (second-price) to n (lowest-price), the worst-case equilibrium welfare strictly increases; notably, the first-price auction (k = 1) achieves optimal worst-case social welfare. This result challenges the conventional belief in the efficiency superiority of second-price auctions and provides a novel theoretical benchmark and efficiency ordering criterion for auction mechanism design.

Technology Category

• Game Theory and Economic Paradigms: Auctions and Market-Based Systems
• Multiagent Systems: Mechanism Design
• Search and Optimization: Combinatorial Optimization

Application Category

• Economics, Online Markets and Human Computation: Advertising auctions, pricing, markets, and exchanges
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

We study $k$-price auctions in a complete information environment and characterize all pure-strategy Nash equilibrium outcomes. In a setting with $n$ agents having ordered valuations, we show that any agent, except those with the lowest $k-2$ valuations, can win in equilibrium. As a consequence, worst-case welfare increases monotonically as we go from $k=2$ (second-price auction) to $k=n$ (lowest-price auction), with the first-price auction achieving the highest worst-case welfare.

Problem

• Characterize Nash equilibria in k-price auctions
• Determine winning agents in ordered valuations
• Analyze welfare impact of varying k-values

Innovation

• Analyzes k-price auctions under complete information
• Characterizes pure-strategy Nash equilibrium outcomes
• Shows worst-case welfare increases with k