Market Equilibria With Buying Rights

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 \textit{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.