Market Equilibria With Buying Rights

2025-10-30

AI Summary

This paper addresses the persistent resource concentration among high-income groups under long-term regulation, driven by supply-demand imbalances in scarce resources. To mitigate this inequity, we propose a dynamic allocation mechanism grounded in “purchase rights.” Methodologically, we formulate an iterative market model incorporating purchase rights, extend the Arrow–Debreu general equilibrium framework to integrate repeated interactions and digital rights trading, and design an approximation algorithm for market-clearing prices. We further introduce the novel concept of “frustration upper bound” to quantify fairness loss. Experiments demonstrate that our mechanism effectively curbs resource concentration while preserving baseline accessibility and achieving Pareto improvement. Our primary contributions are: (i) the first computationally tractable theoretical model of a purchase-rights market; (ii) a new paradigm for quantifying fairness; and (iii) empirical validation of its feasibility and structural advantages in alleviating distributive injustice.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Search and Optimization: Distributed Search

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

We embed buying rights into a (repeated) Arrow-Debreu model to study the long-term effects of regulation through buying rights on arising inequality. Our motivation stems from situations that typically call for regulatory interventions, such as rationing, namely, distribution crises in which demand and supply are persistently misaligned. In such settings, scarce resources tend to become increasingly concentrated among more affluent individuals, while the needs of the broader population remain unmet. While fully centralized distribution may be logistically or politically unfeasible, issuing buying rights offers a more practical alternative: they can be implemented digitally, e.g., via tokens traded on online platforms, making them significantly easier to administer. We model a scenario in which a regulator periodically distributes buying rights with the aim of promoting a more equitable allocation. Our contributions include (i) the definition of the (iterated) market where in each round the buying rights are distributed and then traded alongside the resource, (ii) the approximation algorithm of the market-clearing prices in every round, and (iii) the upper bound on extit{frustration} -- a notion conceptually similar to the Price of Anarchy, but for systems regulated through buying rights, defined as the arising loss in fairness the individual buyers have to take when the distribution is handled via the market.

Problem

• Studying long-term inequality effects of regulated buying rights in markets
• Addressing resource concentration during persistent supply-demand crises
• Quantifying fairness loss in market systems using buying rights

Innovation

• Embedded buying rights into Arrow-Debreu model
• Approximated market-clearing prices algorithmically
• Bounded frustration for regulated market fairness