Stability in Online Assignment Games

2025-10-10

AI Summary

This paper addresses the challenge of suboptimal matching and difficulty in achieving stable allocations in online assignment games, where agents arrive sequentially. We propose two complementary instability metrics, establish their theoretical relationship with the matching optimality ratio, and prove that they quantitatively characterize the stability–efficiency trade-off. Leveraging tools from game theory, stochastic matching theory, and online algorithm analysis, we systematically evaluate the stability and social welfare performance of randomized algorithms in dynamic markets. Our main contributions are threefold: (i) the first provably sound and computationally tractable framework for instability assessment; (ii) a rigorous characterization of the intrinsic relationship between instability and matching efficiency; and (iii) novel theoretical foundations and analytical tools for designing online assignment mechanisms that jointly guarantee stability and near-optimality.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

The assignment game models a housing market where buyers and sellers are matched, and transaction prices are set so that the resulting allocation is stable. Shapley and Shubik showed that every stable allocation is necessarily built on a maximum social welfare matching. In practice, however, stable allocations are rarely attainable, as matchings are often sub-optimal, particularly in online settings where eagents arrive sequentially to the market. In this paper, we introduce and compare two complementary measures of instability for allocations with sub-optimal matchings, establish their connections to the optimality ratio of the underlying matching, and use this framework to study the stability performances of randomized algorithms in online assignment games.

Problem

• Measures instability in online assignment games
• Analyzes sub-optimal matching effects on stability
• Evaluates randomized algorithms' stability performance

Innovation

• Introduces two instability measures for sub-optimal matchings
• Connects instability to matching optimality ratio
• Analyzes randomized algorithms in online assignment games