Mechanisms for Fair Allocation Problems: No-Punishment Payment Rules in Fully Verifiable Settings

TL;DR

This paper introduces new mechanisms for fair allocation of indivisible goods with monetary compensation in settings where verification is possible but not punitive, achieving truthfulness, efficiency, and fairness through Shapley value-based utilities.

Contribution

It proposes a novel mechanism design framework with verification that ensures truthful, efficient, and fair allocations, including polynomial-time randomized variants for practical use.

Findings

Mechanism is truthful, efficient, and budget-balanced.

Verification is used without punishing agents for incorrect declarations.

Two polynomial-time randomized mechanisms are proposed for large-agent scenarios.

Abstract

Mechanism design is addressed in the context of fair allocations of indivisible goods with monetary compensation. Motivated by a real-world social choice problem, mechanisms with verification are considered in a setting where (i) agents' declarations on allocated goods can be fully verified before payments are performed, and where (ii) verification is not used to punish agents whose declarations resulted in incorrect ones. Within this setting, a mechanism is designed that is shown to be truthful, efficient, and budget-balanced, and where agents' utilities are fairly determined by the Shapley value of suitable coalitional games. The proposed mechanism is however shown to be #P-complete. Thus, to deal with applications with many agents involved, two polynomial-time randomized variants are also proposed: one that is still truthful and efficient, and which is approximately budget-balanced with high probability, and another one that is truthful in expectation, while still budget-balanced and efficient.