Shapley Value for Parallel Machine Sequencing Situation without Initial Order

We consider the parallel identical machine sequencing situation without initial schedule. For the situation with identical job processing time, we design a cost allocation rule which gives the Shapley value of the related sequencing game in polynomial time. For the game with identical job weight, we also present a polynomial time procedure to compute the Shapley value.

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Parallel-Batch Scheduling with Two Models of Deterioration to Minimize the Makespan

Abstract and Applied Analysis ◽

10.1155/2014/495187 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10 ◽

Cited By ~ 1

Author(s):

Cuixia Miao

Keyword(s):

Polynomial Time ◽

Single Machine ◽

Processing Time ◽

Parallel Machine ◽

Batch Scheduling ◽

Approximation Schemes ◽

Time Approximation ◽

Identical Parallel Machine ◽

Parallel Machine Problem ◽

Machine Problem

We consider the bounded parallel-batch scheduling with two models of deterioration, in which the processing time of the first model ispj=aj+αtand of the second model ispj=a+αjt. The objective is to minimize the makespan. We presentO(n log n)time algorithms for the single-machine problems, respectively. And we propose fully polynomial time approximation schemes to solve the identical-parallel-machine problem and uniform-parallel-machine problem, respectively.

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Efficient Computation of Semivalues for Game-Theoretic Network Centrality

Journal of Artificial Intelligence Research ◽

10.1613/jair.1.11239 ◽

2018 ◽

Vol 63 ◽

pp. 145-189 ◽

Cited By ~ 1

Author(s):

Mateusz K. Tarkowski ◽

Piotr L. Szczepański ◽

Tomasz P. Michalak ◽

Paul Harrenstein ◽

Michael Wooldridge

Keyword(s):

Polynomial Time ◽

Shapley Value ◽

Centrality Measures ◽

Efficient Computation ◽

Solution Concepts ◽

Banzhaf Index ◽

The Shapley Value ◽

Game Theoretic ◽

Theoretic Solution ◽

Network Centralities

Some game-theoretic solution concepts such as the Shapley value and the Banzhaf index have recently gained popularity as measures of node centrality in networks. While this direction of research is promising, the computational problems that surround it are challenging and have largely been left open. To date there are only a few positive results in the literature, which show that some game-theoretic extensions of degree-, closeness- and betweenness-centrality measures are computable in polynomial time, i.e., without the need to enumerate the exponential number of all possible coalitions. In this article, we show that these results can be extended to a much larger class of centrality measures that are based on a family of solution concepts known as semivalues. The family of semivalues includes, among others, the Shapley value and the Banzhaf index. To this end, we present a generic framework for defining game-theoretic network centralities and prove that all centrality measures that can be expressed in this framework are computable in polynomial time. Using our framework, we present a number of new and polynomial-time computable game-theoretic centrality measures.

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The Concept of the Shapley Value and the Cost Allocation Between Cooperating Participants

Encyclopedia of Information Science and Technology, Fourth Edition ◽

10.4018/978-1-5225-2255-3.ch182 ◽

2018 ◽

pp. 2095-2107 ◽

Cited By ~ 1

Author(s):

Alexander Kolker

Keyword(s):

Game Theory ◽

Shapley Value ◽

Cost Allocation ◽

Bundled Payment ◽

Bundled Payments ◽

Healthcare Settings ◽

The Shapley Value ◽

Mathematical Game ◽

Episodes Of Care ◽

The Cost

The goal of this chapter is to illustrate two mathematical game theory concepts for allocating costs (savings) between cooperating participants, specifically in healthcare settings. These concepts are the nucleolus and the Shapley value. The focus of this chapter is on the practical application of the Shapley value for the cost sharing within the bundled payments model for the episodes of care mandated recently by the Center for Medicare Services (CMS). The general Shapley value methodology is illustrated, as well as an important particular case in which each participant uses only a portion of the largest participant's asset (the so-called airport game). The intended readers are primarily leaders of organizations and hospitals involved in the implementation of the CMS mandated bundled payment model for the episodes of care.

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Complexity of Computing the Shapley Value in Games with Externalities

Proceedings of the AAAI Conference on Artificial Intelligence ◽

10.1609/aaai.v34i02.5601 ◽

2020 ◽

Vol 34 (02) ◽

pp. 2244-2251 ◽

Cited By ~ 1

Author(s):

Oskar Skibski

Keyword(s):

Polynomial Time ◽

Shapley Value ◽

Marginal Contribution ◽

The Shapley Value ◽

Games With Externalities ◽

Computational Properties

We study the complexity of computing the Shapley value in games with externalities. We focus on two representations based on marginal contribution nets (embedded MC-nets and weighted MC-nets) and five extensions of the Shapley value to games with externalities. Our results show that while weighted MC-nets are more concise than embedded MC-nets, they have slightly worse computational properties when it comes to computing the Shapley value: two out of five extensions can be computed in polynomial time for embedded MC-nets and only one for weighted MC-nets.

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A Game Theoretic Approach to the Cost Allocation Problem by Means of the τ-Value, the Nucleolus and the Shapley Value

Theory and Decision Library - Cooperative Games, Solutions and Applications ◽

10.1007/978-94-015-7787-8_4 ◽

1988 ◽

pp. 91-110

Author(s):

Theo Driessen

Keyword(s):

Shapley Value ◽

Cost Allocation ◽

Allocation Problem ◽

Theoretic Approach ◽

The Shapley Value ◽

Game Theoretic ◽

The Cost ◽

Game Theoretic Approach

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The Shapley Value As Applied to Cost Allocation: A Reinterpretation

Journal of Accounting Research ◽

10.2307/2490320 ◽

1979 ◽

Vol 17 (1) ◽

pp. 295 ◽

Cited By ~ 45

Author(s):

Alvin E. Roth ◽

Robert E. Verrecchia

Keyword(s):

Shapley Value ◽

Cost Allocation ◽

The Shapley Value

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The Tractability of the Shapley Value over Bounded Treewidth Matching Games

Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2017/145 ◽

2017 ◽

Cited By ~ 1

Author(s):

Gianluigi Greco ◽

Francesco Lupia ◽

Francesco Scarcello

Keyword(s):

Polynomial Time ◽

Shapley Value ◽

Open Problem ◽

Positive Answer ◽

Coalitional Games ◽

Solution Concepts ◽

Bounded Treewidth ◽

The Shapley Value ◽

Matching Games

Matching games form a class of coalitional games that attracted much attention in the literature. Indeed, several results are known about the complexity of computing over them {solution concepts}. In particular, it is known that computing the Shapley value is intractable in general, formally #P-hard, and feasible in polynomial time over games defined on trees. In fact, it was an open problem whether or not this tractability result holds over classes of graphs properly including acyclic ones. The main contribution of the paper is to provide a positive answer to this question, by showing that the Shapley value is tractable for matching games defined over graphs having bounded treewidth. The proposed technique has been implemented and tested on classes of graphs having different sizes and treewidth at most three.

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