[Paper Review] Strategyproof Quota Mechanisms for Multiple Assignment Problems

Hadi Hosseini, Kate Larson|arXiv (Cornell University)|Jul 25, 2015

Game Theory and Voting Systems37 references4 citations

TL;DR

This paper proposes strategyproof quota mechanisms for multiple assignment problems with lexicographic preferences, showing that serial dictatorship quota mechanisms are the only deterministic mechanisms satisfying strategyproofness, non-bossiness, Pareto efficiency, and neutrality. It further proves that randomized RSDQ mechanisms are strategyproof, ex post efficient, and envyfree for any number of agents, objects, and quota systems under downward lexicographic preferences.

ABSTRACT

We study the problem of allocating multiple objects to agents without transferable utilities, where each agent may receive more than one object according to a quota. Under lexicographic preferences, we characterize the set of strategyproof, non-bossy, and neutral quota mechanisms and show that under a mild Pareto efficiency condition, serial dictatorship quota mechanisms are the only mechanisms satisfying these properties. Dropping the neutrality requirement, this class of quota mechanisms further expands to sequential dictatorship quota mechanisms. We then extend quota mechanisms to randomized settings, and show that the random serial dictatorship quota mechanisms (RSDQ) are envyfree, strategyproof, and ex post efficient for any number of agents and objects and any quota system, proving that the well-studied Random Serial Dictatorship (RSD) satisfies envyfreeness when preferences are lexicographic.

Motivation & Objective

• To design incentive-compatible allocation mechanisms for multiple assignment problems where agents may receive more than one object based on individual quotas.
• To characterize deterministic mechanisms that satisfy strategyproofness, non-bossiness, Pareto efficiency, and neutrality under lexicographic preferences.
• To extend the analysis to randomized mechanisms and establish fairness and strategyproofness properties in stochastic settings.
• To address open questions on the existence of fair and strategyproof mechanisms in multiple assignment domains with variable quotas.
• To demonstrate that RSDQ mechanisms achieve envyfreeness in lexicographic preference domains, even when n ≠ m.

Proposed method

• Characterize the set of strategyproof, non-bossy, and neutral mechanisms under lexicographic preferences using axiomatic analysis.
• Prove that under a mild Pareto efficiency condition, only serial dictatorship quota mechanisms satisfy the required properties.
• Extend the analysis to randomized mechanisms by introducing Random Serial Dictatorship Quota (RSDQ) mechanisms.
• Use lexicographic preference assumptions to derive stochastic symmetry and envyfreeness in randomized allocations.
• Apply downward lexicographic preference structure to prove ex post efficiency and strategyproofness of RSDQ mechanisms.
• Contrast RSDQ with other mechanisms like Probabilistic Serial (PS), showing RSDQ maintains strategyproofness and envyfreeness even when n > m or n < m.

Experimental results

Research questions

• RQ1 Which deterministic quota mechanisms are strategyproof, non-bossy, Pareto efficient, and neutral under lexicographic preferences?
• RQ2 How does the class of such mechanisms change when neutrality is dropped?
• RQ3 Can randomized quota mechanisms achieve envyfreeness while preserving strategyproofness and ex post efficiency?
• RQ4 Is the well-known Random Serial Dictatorship (RSD) mechanism envyfree under lexicographic preferences, and does this hold for any n and m?
• RQ5 Are RSDQ mechanisms the only mechanisms satisfying strategyproofness, ex post efficiency, and envyfreeness in the multiple assignment domain with lexicographic preferences?

Key findings

• Under lexicographic preferences, serial dictatorship quota mechanisms are the only mechanisms satisfying strategyproofness, non-bossiness, Pareto efficiency, and neutrality.
• When neutrality is dropped, the class expands to include sequential dictatorship quota mechanisms.
• Random Serial Dictatorship Quota (RSDQ) mechanisms are strategyproof, ex post C-efficient, and envyfree for any number of agents, objects, and quota systems under downward lexicographic preferences.
• The well-known RSD mechanism is proven to be envyfree under lexicographic preferences, even when the number of agents and objects are unequal (n ≠ m).
• RSDQ mechanisms provide a rich, flexible framework for fair and strategyproof allocation in multiple assignment problems with arbitrary quota systems.
• The results resolve open questions on the existence of mechanisms with favorable fairness and strategyproofness properties in multiple assignment domains.