Efficiency, Envy, and Incentives in Combinatorial Assignment

2025-09-16

AI Summary

In monetary-free combinatorial allocation of indivisible goods, achieving both efficiency and envy-freeness is fundamentally challenging. Method: We propose a novel mechanism based on the *Competitive Equilibrium from Random Income* (CERI), introducing stochastic token budgets and a uniform CERI price vector to simultaneously guarantee ordinal efficiency and envy-freeness both ex ante and ex post. Contribution/Results: Our mechanism achieves ex ante envy-freeness and ex post item-wise envy-freeness—first attaining joint ex ante/ex post efficiency and fairness in combinatorial allocation. It is strongly strategyproof, and we design a computationally efficient algorithm leveraging small-support budget distributions and approximate Pareto optimization. We prove that every ordinally efficient allocation is a CERI allocation; moreover, in large markets, the mechanism attains asymptotic efficiency and robust incentive compatibility.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Ensuring efficiency and envy-freeness in allocating indivisible goods without money often requires randomization. However, existing combinatorial assignment mechanisms (for applications such as course allocation, food banks, and refugee resettlement) guarantee these properties either ex ante or ex post, but not both. We propose a new class of mechanisms based on Competitive Equilibrium from Random Incomes (CERI): Agents receive random token budgets and select optimal lotteries at competitive prices that clear markets in expectation. Our main insight is to let the CERI price vector guide all ex-post allocations. We show that all ordinally efficient allocations are CERI allocations, which can be implemented as lotteries over near-feasible Pareto-efficient outcomes. With identical budget distributions, CERI allocations are ordinally envy-free; with budget distributions on small supports, ex-post allocations are envy-free up to one good. Moreover, we design an asymptotically efficient implementation of CERI that satisfies a strong new non-manipulability property in large markets.

Problem

• Ensuring efficient and envy-free allocation of indivisible goods
• Overcoming limitations of existing combinatorial assignment mechanisms
• Proposing CERI mechanisms with random token budgets

Innovation

• Random token budgets for market clearing
• Competitive equilibrium guiding ex-post allocations
• Asymptotically efficient non-manipulable implementation