Competitive Equilibria with Unequal Budgets: Supporting Arbitrary Pareto Optimal Allocations

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.