Equity in auction design with unit-demand agents and non-quasilinear preferences

TL;DR

The paper studies equity-oriented auction design for unit-demand objects when agents may exhibit income effects (non-quasilinear preferences). It proves that, over the classical domain, the minimum Walrasian equilibrium price (MWEP) mechanism is the unique mechanism satisfying strategy-proofness, ex-post individual rationality, no subsidies, no wastage, and equal treatment of equals. Moreover, the MWEP mechanism is efficient, implying any mechanism meeting these fairness and incentive constraints must be efficient as well. The results provide an equity-based foundation for MWEP in public allocations and show how fairness objectives can effectively substitute for Pareto efficiency under these conditions, with implications for robustness to income effects in bidders. The work links fairness to efficiency in a robust mechanism design setting and suggests further study of restricted domains, such as quasilinear preferences, where the characterization may differ.

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.

Figures (14)

• Figure 1: An indifference vector
• Figure 2: A preference and its indifference vectors
• Figure 3: An illustration of $R'_1$.
• Figure 4: An illustration of $R'_2$.
• Figure 5: An illustration of $R"$.