An axiomatic approach to characterizing and relaxing strategyproofness of one-sided matching mechanisms

Abstract

The one-sided matching problem is concerned with the allocation of indivisible goods to self-interested agents with privately known preferences. Monetary transfers are not permitted, which makes this problem different from auctions and other settings with transferable utility. In practice, such problems often arise in situations that are of great importance to peoples' lives. For example, students must be matched to schools, teachers to training programs, or houses to tenants. While strategyproofness is certainly a desirable design desideratum, it is also a severe restriction when other properties are important, such as efficiency or fairness. We study ordinal mechanisms for this problem, where agents have vNM utility functions over the objects. The paper makes two main contributions: we 1. characterize strategyproof one-sided matching mechanisms by three intuitive axioms, and we 2. propose the partial strategyproofness concept, a relaxation of strategyproofness, which bridges the long-standing gap between full and weak strategyproofness. CHARACTERIZATION OF STRATEGYPROOF MECHANISMSOur first contribution is to show that strategyproof mechanisms are characterized by three intuitive axioms. To understand the axioms, suppose an agent is considering whether to report truthfully or swap two adjacent objects, e.g., a b to b a:(1) A mechanism is swap monotonic if upon such a swap, the reporting agent's allocation either does not change at all, or the allocation for b strictly increases and the allocation for a strictly decreases.(2) A mechanism is upper invariant if the allocation does not change for any object that the agent strictly prefers to a, i.e., any object in the upper contour set of a.(3) The mechanism is lower invariant if the allocation does not change for any object that the agent likes strictly less than b, i.e., any object in the lower contour set of b.We show that a mechanism is strategyproof if and only if it is swap monotonic, upper invariant, and lower invariant. Thus, strategyproofness requires that the mechanism only affects the allocation of the objects that are swapped (if any), and the direction of this change must be consistent with the agent's reported preferences.

Bounded Incentives in Manipulating the Probabilistic Serial Rule

“…In the presence of incentives, the random assignment problem has been extensively studied in Computer Science and Economics over the years (Zhou 1990;Dughmi and Ghosh 2010;Mennle and Seuken 2014). We refer the interested reader to surveys (Abdulkadiroglu and Sönmez 2013;Sönmez andÜnver 2011).…”

Estimating Approximate Incentive Compatibility

“…At a high level, a mechanism is incentive compatible if no agent can ever increase her utility by misreporting her type. A mechanism is γ-incentive compatible if each agent can increase her utility by an additive factor of at most γ by misreporting her type [Kothari et al, 2003, Archer et al, 2004, Conitzer and Sandholm, 2007, Dekel et al, 2010, Lubin and Parkes, 2012, Mennle and Seuken, 2014, Dütting et al, 2015, Azevedo and Budish, 2018, Feng et al, 2018, Golowich et al, 2018, Dütting et al, 2019. In the main body of this paper, we concentrate on ex-interim approximate incentive compatibility [Azevedo andBudish, 2018, Lubin andParkes, 2012].…”

“…Due in part to the ubiquity of manipulable mechanisms, a growing body of additional research has explored mechanisms that are not incentive compatible [Kothari et al, 2003, Archer et al, 2004, Conitzer and Sandholm, 2007, Dekel et al, 2010, Lubin and Parkes, 2012, Mennle and Seuken, 2014, Dütting et al, 2015, Azevedo and Budish, 2018, Golowich et al, 2018, Dütting et al, 2019, Feng et al, 2018. A popular and widely-studied relaxation of incentive compatibility is γ-incentive compatibility [Kothari et al, 2003, Archer et al, 2004, Dekel et al, 2010, Lubin and Parkes, 2012, Mennle and Seuken, 2014, Dütting et al, 2015, Azevedo and Budish, 2018, which requires that no agent can improve his utility by more than γ when he misreports his type.…”

Computational Social Choice: The First Ten Years and Beyond

“…Bogomolnaia and Moulin [29] have shown that no random assignment rule satisfies SD-efficiency, strong SD-strategyproofness and equal treatments of equals (agents with identical preferences receive identical individual random assignments), even when individual preferences are strict. The tradeoff among these properties is the subject of ongoing research (e.g., [5,99]).…”