On Strategy-Proof Allocation without Payments or Priors

Han, Li; Su, Chunzhi; Tang, Linpeng; Zhang, Hongyang

doi:10.1007/978-3-642-25510-6_16

Cited by 9 publications

(13 citation statements)

References 10 publications

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“…This result carries over to the wagering setting, and complements the impossibility result of Freeman, Pennock, and Vaughan (2017) that no weakly budget-balanced wagering mechanism can simultaneously satisfy incentive compatibility, side-bet Pareto optimality, and individual rationality. As another example, Han et al (2011) showed that, for large enough n, no incentive compatible allocation mechanism can achieve better than a 1/m approximation to the optimal social welfare. This result also carries over to wagering.…”

Section: Discussionmentioning

confidence: 99%

An Equivalence between Wagering and Fair-Division Mechanisms

Freeman

Pennock

Vaughan

2019

AAAI

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We draw a surprising and direct mathematical equivalence between the class of allocation mechanisms for divisible goods studied in the context of fair division and the class of weakly budget-balanced wagering mechanisms designed for eliciting probabilities. The equivalence rests on the intuition that wagering is an allocation of financial securities among bettors, with a bettor’s value for each security proportional to her belief about the likelihood of a future event. The equivalence leads to theoretical advances and new practical approaches for both fair division and wagering. Known wagering mechanisms based on proper scoring rules yield fair allocation mechanisms with desirable properties, including the first strictly incentive compatible fair-division mechanism. At the same time, allocation mechanisms make for novel wagering rules, including one that requires only ordinal uncertainty judgments and one that outperforms existing rules in a range of simulations.

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Section: Discussionmentioning

confidence: 99%

An Equivalence between Wagering and Fair-Division Mechanisms

Freeman

Pennock

Vaughan

2019

AAAI

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“…Han et al [HSTZ11] showed a number of upper bound results on the competitiveness of SP mechanisms, when the numbers of agents and/or items increase. In particular, they showed that no swap-dictatorial mechanism can be better than 1 2 + o m (1) -competitive for m items.…”

Section: Related Workmentioning

confidence: 99%

Better Strategyproof Mechanisms without Payments or Prior --- An Analytic Approach

Cheung

2016

Preprint

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We revisit the problem of designing strategyproof mechanisms for allocating divisible items among two agents who have linear utilities, where payments are disallowed and there is no prior information on the agents' preferences. The objective is to design strategyproof mechanisms which are competitive against the most efficient (but not strategyproof) mechanism.For the case with two items:• We provide a set of sufficient conditions for strategyproofness.• We use an analytic approach to derive strategyproof mechanisms which are more competitive than all prior strategyproof mechanisms.• We improve the linear-program-based proof of Guo and Conitzer [GC10] to show new upper bounds on competitive ratios.• We provide the first compact proof on upper bound of competitiveness.For the cases with any number of items, we build on the Partial Allocation mechanisms introduced by Cole et al. [CGG13a,CGG13b] to design a strategyproof mechanism which is 0.67776-competitive, breaking the 2 3 barrier. We also propose a new sub-class of strategyproof mechanisms for any numbers of agents and items, which we call it Dynamic-Increasing-Price mechanisms, where each agent purchases the items using virtual money, and the prices of the items depend on other agents' preferences.

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“…The recent papers of Guo and Conitzer [16] and of Han et al [18] also consider the truthful allocation of multiple divisible goods; they focus on additive linear valuations and their goal is to maximize the social welfare (or efficiency) after scaling every player's reported valuations so that her total valuation for all items is 1. Guo and Conitzer [16] study two-agent instances, providing both upper and lower bounds for the achievable approximation; Han et al [18] extend these results and also study the multiple agents setting.…”

Section: Related Workmentioning

confidence: 99%

“…Guo and Conitzer [16] study two-agent instances, providing both upper and lower bounds for the achievable approximation; Han et al [18] extend these results and also study the multiple agents setting. For problem instances that may involve an arbitrary number of items both papers provide negative results: no non-trivial approximation factor can be achieved by any truthful mechanism when the number of players is also unbounded.…”

Section: Related Workmentioning

confidence: 99%

“…For problem instances that may involve an arbitrary number of items both papers provide negative results: no non-trivial approximation factor can be achieved by any truthful mechanism when the number of players is also unbounded. For the two-player case, after Guo and Conitzer [16] studied some classes of dictatorial mechanisms, Han et al [18] showed that no dictatorial mechanism can guarantee more than the trivial 0.5 factor. Interestingly, we recently showed [10] that combining a special two-player version of the Partial Allocation mechanism with a dictatorial mechanism can actually beat this bound, achieving a 0.622 approximation.…”

Section: Related Workmentioning

confidence: 99%

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Mechanism design for fair division

Cole

Gkatzelis

Goel

2013

Proceedings of the Fourteenth ACM Conference on Electronic Commerce

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We revisit the classic problem of fair division from a mechanism design perspective and provide an elegant truthful mechanism that yields surprisingly good approximation guarantees for the widely used solution of Proportional Fairness. This solution, which is closely related to Nash bargaining and the competitive equilibrium, is known to be not implementable in a truthful fashion, which has been its main drawback. To alleviate this issue, we propose a new mechanism, which we call the Partial Allocation mechanism, that discards a carefully chosen fraction of the allocated resources in order to incentivize the agents to be truthful in reporting their valuations.For a multi-dimensional domain with an arbitrary number of agents and items, and for the very large class of homogeneous valuation functions, we prove that our mechanism provides every agent with at least a 1/e ≈ 0.368 fraction of her Proportionally Fair valuation. To the best of our knowledge, this is the first result that gives a constant factor approximation to every agent for the Proportionally Fair solution. To complement this result, we show that no truthful mechanism can guarantee more than 0.5 approximation, even for the restricted class of additive linear valuations. We also uncover a connection between the Partial Allocation mechanism and VCG-based mechanism design, which introduces a way to implement interesting truthful mechanisms in settings where monetary payments are not an option.We also ask whether better approximation ratios are possible in more restricted settings. In particular, motivated by the massive privatization auction in the Czech republic in the early 90s we provide another mechanism for additive linear valuations that works really well when all the items are highly demanded.

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On Strategy-Proof Allocation without Payments or Priors

Cited by 9 publications

References 10 publications

An Equivalence between Wagering and Fair-Division Mechanisms

An Equivalence between Wagering and Fair-Division Mechanisms

Better Strategyproof Mechanisms without Payments or Prior --- An Analytic Approach

Mechanism design for fair division

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