Redistribution Mechanisms for Assignment of Heterogeneous Objects

This paper is about allocation of an infinitely divisible good to several rational and strategic agents. The allocation is done by a social planner who has limited information because the agents' valuation functions are taken to be private information known only to the respective agents. We allow only a scalar signal, called a bid, from each agent to the social planner. Yang and Hajek [25] and Johari and Tsitsiklis [16] proposed a scalar strategy VickreyClarke-Groves (SSVCG) mechanism with efficient Nash equilibria. We consider a setting where the social planner desires minimal budget surplus. Example situations include fair sharing of Internet resources and auctioning of certain public goods where revenue maximization is not a consideration. Under the SSVCG framework, we propose a mechanism that is efficient and comes close to budget balance by returning much of the payments back to the agents in the form of rebates. We identify a design criterion for almost budget balance, impose feasibility and voluntary participation constraints, simplify the constraints, and arrive at a convex optimization problem to identify the parameters of the rebate functions. The convex optimization problem has a linear objective function and a continuum of linear constraints. We propose a solution method that involves a finite number of constraints, and identify the number of samples sufficient for a good approximation.

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“…as net surplus without regard to the absolute value of the payment amounts. A rewriting of Moulin's objective (9) as…”

Section: Design For the Worst Casementioning

confidence: 99%

“…Guo and Conitzer [11] and Moulin [20] studied rebate design in the case of discrete goods. Gujar and Narahari [9,10] studied rebate design for the allocation of m heterogeneous discrete goods among n agents. Chorppath et al [5] studied rebate design in the divisible goods setting.…”

Section: Introductionmentioning

confidence: 99%

Almost budget balanced mechanisms with scalar bids for allocation of a divisible good

Thirumulanathan

Vinay²,

Bhashyam

et al. 2017

European Journal of Operational Research

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“…So far, several multi-unit auction mechanisms for budget constrained participants have been proposed [1], [2], [6], [15]. In addition, redistribution mechanisms have recently attracted considerable attention from the AI and agent research community [3], [4], [7], [9], [10], [11], [12]. However, to the best of our knowledge, no redistribution mechanism has been developed for budget-constrained participants, although having a budget constraint is quite realistic and natural.…”

Section: Introductionmentioning

confidence: 99%

Generalized Partition Mechanism: Framework for Combining Multiple Strategy-Proof Mechanisms

Sakurai

Yokoo

2012

2012 IEEE/WIC/ACM International Conferences on Web Intelligence and Intelligent Agent Technology

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This paper presents a framework for combining multiple strategy-proof resource allocation mechanisms, in which participants are divided into several groups (partitions) and each mechanism is applied to one partition. The idea of dividing participants into several groups is introduced to achieve budget balance in a redistribution mechanism, i.e., the payment (money) collected in one partition is distributed in another partition. Furthermore, this idea has been used to adjust parameters of a mechanism (e.g., the reservation price in an auction) based on the information of participants in one partition in order to improve the mechanism's efficiency or revenue. This paper presents a unified framework called a generalized partition mechanism, in which information, money, and unsold goods can be transferred among partitions. This framework is very general and thus can be applied to various settings, including cases where a redistribution mechanism must adjust parameters to obtain a better social surplus. We provide a sufficient condition on the flow of information, money, and goods among partitions so that the generalized partition mechanism is strategy-proof, assuming that each mechanism applied to the partition is strategy-proof. We can use this sufficient condition as a guideline for combining multiple mechanisms. To show the applicability of this guideline, we develop new redistribution mechanisms based on this guideline, in which the utility of a participant can be non-quasi-linear.

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“…. This notion of worst-case optimality was also studied for more general settings(Gujar & Narahari, 2011;Guo, 2011Guo, , 2012. 4.…”

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confidence: 99%

Undominated Groves Mechanisms

Guo¹,

Markakis²,

Apt³

et al. 2013

jair

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The family of Groves mechanisms, which includes the well-known VCG mechanism (also known as the Clarke mechanism), is a family of efficient and strategy-proof mechanisms. Unfortunately, the Groves mechanisms are generally not budget balanced. That is, under such mechanisms, payments may flow into or out of the system of the agents, resulting in deficits or reduced utilities for the agents. We consider the following problem: within the family of Groves mechanisms, we want to identify mechanisms that give the agents the highest utilities, under the constraint that these mechanisms must never incur deficits. We adopt a prior-free approach. We introduce two general measures for comparing mechanisms in prior-free settings. We say that a non-deficit Groves mechanism M individually dominates another non-deficit Groves mechanism M' if for every type profile, every agent's utility under M is no less than that under M', and this holds with strict inequality for at least one type profile and one agent. We say that a non-deficit Groves mechanism M collectively dominates another non-deficit Groves mechanism M' if for every type profile, the agents' total utility under M is no less than that under M', and this holds with strict inequality for at least one type profile. The above definitions induce two partial orders on non-deficit Groves mechanisms. We study the maximal elements corresponding to these two partial orders, which we call the individually undominated mechanisms and the collectively undominated mechanisms, respectively.

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Redistribution Mechanisms for Assignment of Heterogeneous Objects

Cited by 16 publications

References 18 publications

Almost budget balanced mechanisms with scalar bids for allocation of a divisible good

Almost budget balanced mechanisms with scalar bids for allocation of a divisible good

Generalized Partition Mechanism: Framework for Combining Multiple Strategy-Proof Mechanisms

Undominated Groves Mechanisms

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