Strategy-Proof and Fair Assignment is Wasteful

Martini, Giorgio

doi:10.2139/ssrn.2615389

Cited by 4 publications

(7 citation statements)

References 3 publications

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“…In fact, Bogomolnaia & Moulin (2001) showed that no mechanism can satisfy ordinal efficiency, strategy-proofness and anonymity at the same time. More generally, the extent to which probabilistic assignments can satisfy certain combinations of properties has been widely studied in the literature, leading to an interesting series of impossibility results (Athanassoglou & Sethuraman, 2011;Bogomolnaia & Moulin, 2001;Martini, 2016;Nesterov, 2017;Ramezanian & Feizi, 2022;Zhou, 1990).…”

Section: Mechanisms and Their Propertiesmentioning

confidence: 99%

A pessimist’s approach to one-sided matching

Demeulemeester

Goossens

Hermans

et al. 2023

European Journal of Operational Research

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Section: Mechanisms and Their Propertiesmentioning

confidence: 99%

A pessimist’s approach to one-sided matching

Demeulemeester

Goossens

Hermans

et al. 2023

European Journal of Operational Research

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“…But in some environments there are reasons to focus on non-strategy-proof mechanisms because strategy-proofness conflicts with other important goals. For example, in the object assignment model, several papers have demonstrated the conflict between efficiency, fairness, and strategy-proofness (Zhou, 1990;Bogomolnaia and Moulin, 2001;Martini, 2016;Nesterov, 2017). When efficiency and fairness are primary goals, we have to give up strategyproofness.…”

Section: Truncation-invariant Mechanismmentioning

confidence: 99%

“…The proof of Proposition 1 relies only on the two invariance properties. Martini (2016) has proved that an IR and strategy-proof mechanism that satisfies ETE must be wasteful. In Proposition 1, ExPE of ψ is necessary for proving that ψ ′ is strongly bidominated.…”

Section: Stochastic Dominance In the Object Assignment Problemmentioning

confidence: 99%

“…Kesten and Kurino (2019) prove that even if exogenous outside options are eliminated, as long as students can arbitrarily rank schools in preferences, some schools will endogenously play the role of outside options. 4 In the random assignment model, Martini (2016) proves that every IR and strategy-proof mechanism that treats equals equally is wasteful. This result answers an open question of Erdil (2014).…”

Section: Introductionmentioning

confidence: 99%

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Strategy-proof allocation with outside option

Zhang¹

2020

Preprint

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We consider strategy-proof mechanisms to solve allocation problems where agents can choose outside options if they wish. Mechanisms could return an allocation or a randomization over allocations. We prove two useful theorems, relying on an invariance property of the allocations found by strategy-proof mechanisms when agents vary the ranking of outside options in their preferences. The first theorem proves that, among individually rational and strategy-proof mechanisms, pinning down every agent's probability of choosing outside option in every preference profile is equivalent to pinning down a mechanism. The second theorem provides a sufficient condition for proving equivalence between two strategy-proof mechanisms when the number of possible allocations is finite. The two theorems provide a unified foundation for existing results in several distinct models and imply new results in some models.

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“…Unfortunately, a growing body of work (Bogomolnaia and Moulin, 2001;Martini, 2016;Nesterov, 2017;Zhou, 1990) has demonstrated the inherent incompatibility between efficiency, A mechanism is ordinally efficient if its outcome is not first-order stochastically dominated by any other random assignment.…”

Section: Introductionmentioning

confidence: 99%

Strategy-proof and Envy-free Mechanisms for House Allocation

Shende¹,

Purohit²

2020

Preprint

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We consider the problem of allocating indivisible objects to agents when agents have strict preferences over objects. There are inherent trade-offs between competing notions of efficiency, fairness and incentives in assignment mechanisms. It is, therefore, natural to consider mechanisms that satisfy two of these three properties in their strongest notions, while trying to improve on the third dimension. In this paper, we are motivated by the following question: Is there a strategy-proof and envy-free random assignment mechanism more efficient than equal division? Our contributions in this paper are twofold. First, we further explore the incompatibility between efficiency and envy-freeness in the class of strategy-proof mechanisms. We define a new notion of efficiency that is weaker than ex-post efficiency and prove that any strategyproof and envy-free mechanism must sacrifice efficiency even in this very weak sense. Next, we introduce a new family of mechanisms called Pairwise Exchange mechanisms and make the surprising observation that strategy-proofness is equivalent to envy-freeness within this class.We characterize the set of all neutral and strategy-proof (and hence, also envy-free) mechanisms in this family and show that they admit a very simple linear representation.

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Strategy-Proof and Fair Assignment is Wasteful

Cited by 4 publications

References 3 publications

A pessimist’s approach to one-sided matching

A pessimist’s approach to one-sided matching

Strategy-proof allocation with outside option

Strategy-proof and Envy-free Mechanisms for House Allocation

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