[論文レビュー] Equity in auction design with unit-demand agents and non-quasilinear preferences

Tomoya Kazumura, Debasis Mishra+1 more|arXiv (Cornell University)|Feb 18, 2026

Auction Theory and Applications被引用数 0

ひとこと要約

要約: The paper proves that, with unit-demand agents and non-quasilinear preferences, the minimum Walrasian equilibrium price (MWEP) mechanism is the unique mechanism that is strategy-proof, individually rational, equal-treatment-of-equals, no-wastage, and no-subsidy, on the classical domain.

ABSTRACT

We study a model of auction design where a seller is selling a set of objects to a set of agents who can be assigned no more than one object. Each agent's preference over (object, payment) pair need not be quasilinear. If the domain contains all classical preferences, we show that there is a unique mechanism, the minimum Walrasian equilibrium price (MWEP) mechanism, which is strategy-proof, individually rational, and satisfies equal treatment of equals, no-wastage (every object is allocated to some agent), and no-subsidy (no agent is subsidized). This provides an equity-based characterization of the MEWP mechanism, and complements the efficiency-based characterization of the MWEP mechanism known in the literature.

研究の動機と目的

• Motivates fair auction design in public allocations where agents may face income effects.
• Models multiple heterogeneous objects with unit-demand and non-quasilinear preferences.
• Shows MWEP is the unique mechanism satisfying key fairness and incentive properties on the classical domain.
• Links fairness (ETE) to efficiency and positions MWEP as an equity-based characterization of Walrasian outcomes.
• Highlights implications for policy-friendly auction formats in public contexts.

提案手法

• Defines classical preferences with income effects and non-quasilinear payoffs.
• Introduces Walrasian equilibrium concepts and minimum Walrasian equilibrium price vectors.
• Forms the MWEP mechanism as selecting any allocation supported by a minimum Walrasian equilibrium.
• Proves that any mechanism satisfying strategy-proofness, IR, ETE, NW, NS must be MWEP on the classical domain.
• Utilizes indifference-vector representations to structure the proof and leverage preference richness.

Figure 1: An indifference vector

実験結果

リサーチクエスチョン

• RQ1 Is the MWEP mechanism the unique mechanism satisfying strategy-proofness, IR, ETE, NW, and NS on the classical domain?
• RQ2 Does equal treatment of equals, together with no wastage, imply efficiency under standard incentive constraints?
• RQ3 How does fairness (ETE) interact with efficiency in non-quasilinear, unit-demand auction settings?

主な発見

• On the classical domain, the MWEP mechanism is the unique mechanism that satisfies strategy-proofness, IR, ETE, NW, and NS.
• MWEP is efficient, and any mechanism meeting the five properties must be efficient (Corollary).
• Fairness-based characterization complements efficiency-based views of MWEP in prior literature.
• MWEP remains uniquely characterized even with heterogeneous objects and income effects in agents’ preferences.
• The results highlight that equity (ETE) can substitute for certain efficiency criteria under the given axioms.

Figure 2: A preference and its indifference vectors