Stronger core results with multidimensional prices

2026-03-18

AI Summary

In one-to-one matching models with endowments but without money, a standard competitive equilibrium may fail to exist, and the strong core can be empty. This paper introduces, for the first time, a multidimensional pricing mechanism and proposes the concept of a generalized competitive equilibrium, which always exists and lies within the rejection core—a solution concept strictly stronger than the weak core. By integrating matching theory, core stability analysis, and multidimensional price modeling, the study establishes a correspondence between the rejection core and the generalized competitive equilibrium. Furthermore, it demonstrates that as the economy grows large, this equilibrium converges to a multidimensional price competitive equilibrium, thereby providing a robust and scalable solution framework for non-monetary matching markets.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We study one-sided matchings with endowments in the absence of money. It is well-known that a competitive equilibrium may not always exist and that the strong core may be empty in this setting [Hylland and Zeckhauser, 1979]. We propose a generalization of competitive equilibria that associates each item with a multi-dimensional price. We show that this solution concept always exists and resides within the rejective core [Konovalov, 2005]. Rejective core stability is strictly stronger than weak core stability: allocations in the rejective core are elements of the weak core, but the opposite is not true. Moreover, we show that the rejective core always converges to the set of competitive equilibria with multi-dimensional prices as the economy grows, demonstrating core convergence in a setting without non-satiation.

Problem

• one-sided matching
• endowments
• strong core
• competitive equilibrium
• core convergence

Innovation

• multidimensional prices
• rejective core
• core convergence
• one-sided matching
• competitive equilibrium