A Truthful Cardinal Mechanism for One-Sided Matching

Abebe, Rediet; Cole, Richard; Gkatzelis, Vasilis; Hartline, Jason D.

doi:10.1137/1.9781611975994.129

Cited by 9 publications

(3 citation statements)

References 35 publications

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“…An interesting recent paper [ACGH20] defines the notion of a random partial improvement mechanism for a one-sided matching market. This mechanism truthfully elicits the cardinal preferences of the agents and outputs a distribution over matchings that approximates every agent's utility in the Nash bargaining solution.…”

Section: Related Resultsmentioning

confidence: 99%

Combinatorial Algorithms for Matching Markets via Nash Bargaining: One-Sided, Two-Sided and Non-Bipartite

Panageas¹,

Tröbst²,

Vazirani³

2021

Preprint

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This paper is an attempt to deal with the recent realization [VY21] that the Hylland-Zeckhauser mechanism, which has remained a classic in economics for one-sided matching markets, is likely to be highly intractable. HZ uses the power of a pricing mechanism, which has endowed it with nice game-theoretic properties.[HV21] define a rich collection of Nash-bargaining-based models for one-sided and twosided matching markets, in both Fisher and Arrow-Debreu settings, together with implementations using available solvers, and very encouraging experimental results. This naturally raises the question of finding efficient combinatorial algorithms for these models.In this paper, we give efficient combinatorial algorithms based on the techniques of multiplicative weights update (MWU) and conditional gradient descent (CGD) for several onesided and two-sided models defined in [HV21]. Additionally, we define for the first time a Nash-bargaining-based model for non-bipartite matching markets and solve it using CGD. Furthermore, in every case, we study not only the Fisher but also the Arrow-Debreu version; the latter is also called the exchange version. We give natural applications for each model studied. These models inherit the game-theoretic and computational properties of Nash bargaining.We also establish a deep connection between HZ and the Nash-bargaining-based models, thereby confirming that the alternative to HZ proposed in [HV21] is a principled one.

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Section: Related Resultsmentioning

confidence: 99%

Combinatorial Algorithms for Matching Markets via Nash Bargaining: One-Sided, Two-Sided and Non-Bipartite

Panageas¹,

Tröbst²,

Vazirani³

2021

Preprint

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“…Another example of a non-downward closed setting is one-sided matching markets in which every agent must be matched with exactly one good. An example of a one-sided matching market is the fair housing allocation studied by Abebe et al (2019). Finally, the facility location problem from Devanur, Mihail, and Vazirani (2005) also not downward closed.…”

Section: Related Workmentioning

confidence: 99%

Limitations of Incentive Compatibility on Discrete Type Spaces

Lundy

2020

AAAI

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In the design of incentive compatible mechanisms, a common approach is to enforce incentive compatibility as constraints in programs that optimize over feasible mechanisms. Such constraints are often imposed on sparsified representations of the type spaces, such as their discretizations or samples, in order for the program to be manageable. In this work, we explore limitations of this approach, by studying whether all dominant strategy incentive compatible mechanisms on a set T of discrete types can be extended to the convex hull of T.Dobzinski, Fu and Kleinberg (2015) answered the question affirmatively for all settings where types are single dimensional. It is not difficult to show that the same holds when the set of feasible outcomes is downward closed. In this work we show that the question has a negative answer for certain non-downward-closed settings with multi-dimensional types. This result should call for caution in the use of the said approach to enforcing incentive compatibility beyond single-dimensional preferences and downward closed feasible outcomes.

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“…The consensus allocation is very inefficient; there are better mechanisms for truthful fair division: Cole, Gkatzelis, and Goel (2013b), Cole et al (2013a), Abebe, Cole, Gkatzelis, and Hartline (2019). While these mechanisms do not guarantee Pareto-optimality, they provide a constant-factor approximation to certain measures of social welfare.…”

Section: Truthful Division and Non-pareto-optimal Goalsmentioning

confidence: 99%

Efficient Fair Division with Minimal Sharing

Sandomirskiy¹,

Segal-Halevi²

2019

Preprint

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A set of objects, some goods and some bads, is to be divided fairly among agents with different tastes, modeled by additive utility-functions. If the objects cannot be shared, so that each of them must be entirely allocated to a single agent, then fair division may not exist. What is the smallest number of objects that must be shared between two or more agents in order to attain a fair division?We focus on Pareto-optimal, envy-free and/or proportional allocations. We show that, for a generic instance of the problem -all instances except of a zero-measure set of degenerate problems -a fair and Pareto-optimal division with the smallest possible number of shared objects can be found in polynomial time, assuming that the number of agents is fixed. The problem becomes computationally hard for degenerate instances, where the agents' valuations are aligned for many objects. * This work was inspired by Achikam Bitan, Steven Brams and Shahar Dobzinski, who expressed their dissatisfaction with the current trend of approximate-fairness (SCADA conference, Weizmann Institute, Israel 2018). We are grateful to participants of De Aequa Divisione Workshop on Fair Division (LUISS, Rome, 2019) and the Workshop on Theoretical Aspects of Fairness (WTAF, Patras, 2019) for their comments. Suggestions of Herve Moulin, Antonio Nicolo, and Nisarg Shah were especially useful. Several members of the theoretical-computer-science stackexchange network (http://cstheory.stackexchange.com) provided very helpful answers, in particular: D.

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A Truthful Cardinal Mechanism for One-Sided Matching

Cited by 9 publications

References 35 publications

Combinatorial Algorithms for Matching Markets via Nash Bargaining: One-Sided, Two-Sided and Non-Bipartite

Combinatorial Algorithms for Matching Markets via Nash Bargaining: One-Sided, Two-Sided and Non-Bipartite

Limitations of Incentive Compatibility on Discrete Type Spaces

Efficient Fair Division with Minimal Sharing

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