Competitive Equilibria with Unequal Budgets: Supporting Arbitrary Pareto Optimal Allocations

TL;DR

This paper develops a framework for supporting any Pareto efficient allocation in markets with agents having unequal budgets and additive valuations, using anonymous prices and efficient algorithms, including max-min allocations.

Contribution

It introduces methods to support arbitrary Pareto optimal allocations with unequal budgets and provides computationally efficient algorithms for implementation.

Findings

Supports any Pareto efficient allocation in equilibrium.

Provides algorithms for implementing max-min allocations.

Ensures equilibrium with anonymous prices and agent-specific budgets.

Abstract

We consider a market setting of agents with additive valuations over heterogeneous divisible resources. Agents are assigned a budget of tokens (possibly unequal budgets) they can use to obtain resources; leftover tokens are worthless. We show how to support any Pareto efficient allocation in equilibrium, using anonymous resource prices and agent specific budgets. We also give computationally efficient algorithms for those tasks. In particular, this allows us to support the Rawlsian max-min allocation.