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

2018 ◽  
pp. 2095-2107 ◽  
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.

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

2019 ◽  
pp. 624-639
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.

scholarly journals A Study of Proxies for Shapley Allocations of Transport Costs

2016 ◽  
Vol 56 ◽  
pp. 573-611 ◽  
Author(s):  
Haris Aziz ◽  
Casey Cahan ◽  
Charles Gretton ◽  
Philip Kilby ◽  
Nicholas Mattei ◽  
...  
Keyword(s):  
Shapley Value ◽  
Cost Allocation ◽  
Constant Factor ◽  
Transport Costs ◽  
Total Cost ◽  
The Shapley Value ◽  
Rules Of Thumb ◽  
Cost To Serve ◽  
Problem Instances ◽  
The Cost

We survey existing rules of thumb, propose novel methods, and comprehensively evaluate a number of solutions to the problem of calculating the cost to serve each location in a single-vehicle transport setting. Cost to serve analysis has applications both strategically and operationally in transportation settings. The problem is formally modeled as the traveling salesperson game (TSG), a cooperative transferable utility game in which agents correspond to locations in a traveling salesperson problem (TSP). The total cost to serve all locations in the TSP is the length of an optimal tour. An allocation divides the total cost among individual locations, thus providing the cost to serve each of them. As one of the most important normative division schemes in cooperative games, the Shapley value gives a principled and fair allocation for a broad variety of games including the TSG. We consider a number of direct and sampling-based procedures for calculating the Shapley value, and prove that approximating the Shapley value of the TSG within a constant factor is NP-hard. Treating the Shapley value as an ideal baseline allocation, we survey six proxies for it that are each relatively easy to compute. Some of these proxies are rules of thumb and some are procedures international delivery companies use(d) as cost allocation methods. We perform an experimental evaluation using synthetic Euclidean games as well as games derived from real-world tours calculated for scenarios involving fast-moving goods; where deliveries are made on a road network every day. We explore several computationally tractable allocation techniques that are good proxies for the Shapley value in problem instances of a size and complexity that is commercially relevant.

Query Games in Databases

2021 ◽  
Vol 50 (1) ◽  
pp. 78-85
Author(s):  
Ester Livshits ◽  
Leopoldo Bertossi ◽  
Benny Kimelfeld ◽  
Moshe Sebag
Keyword(s):  
Game Theory ◽  
Cooperative Game ◽  
Shapley Value ◽  
Cooperative Game Theory ◽  
The Shapley Value ◽  
Computational Aspects ◽  
Aggregate Query ◽  
Boolean Query

Database tuples can be seen as players in the game of jointly realizing the answer to a query. Some tuples may contribute more than others to the outcome, which can be a binary value in the case of a Boolean query, a number for a numerical aggregate query, and so on. To quantify the contributions of tuples, we use the Shapley value that was introduced in cooperative game theory and has found applications in a plethora of domains. Specifically, the Shapley value of an individual tuple quantifies its contribution to the query. We investigate the applicability of the Shapley value in this setting, as well as the computational aspects of its calculation in terms of complexity, algorithms, and approximation.

Shapley Ranking of Wines

2012 ◽  
Vol 7 (2) ◽  
pp. 169-180 ◽  
Author(s):  
Victor Ginsburgh ◽  
Israël Zang
Keyword(s):  
Game Theory ◽  
Unique Solution ◽  
Cooperative Game ◽  
Shapley Value ◽  
Rank Order ◽  
Jel Classification ◽  
Ranking Method ◽  
The Shapley Value ◽  
Shapley Values

AbstractWe suggest a new game-theory-based ranking method for wines, in which the Shapley Value of each wine is computed, and wines are ranked according to their Shapley Values. Judges should find it simpler to use, since they are not required to rank order or grade all the wines, but merely to choose the group of those that they find meritorious. Our ranking method is based on the set of reasonable axioms that determine the Shapley Value as the unique solution of an underlying cooperative game. Unlike in the general case, where computing the Shapley Value could be complex, here the Shapley Value and hence the final ranking, are straightforward to compute. (JEL Classification: C71, D71, D78)

A Shapley Value Analysis of the Proposed Canadian Constitutional Amendment Scheme

1973 ◽  
Vol 6 (1) ◽  
pp. 140-143 ◽  
Author(s):  
D.R. Miller
Keyword(s):  
Game Theory ◽  
Shapley Value ◽  
Constitutional Amendment ◽  
Value Analysis ◽  
A Value ◽  
The Shapley Value ◽  
Relative Value ◽  
Individual Player

The interactions of a group of non-identical voting units may be studied by applying the concept of the Shapley value from n-person co-operative game theory. In this theory one assumes that voting units, or players, may form coalitions of various kinds in order to achieve success in the game, and one may assign a “value” to each such coalition based on what it can accomplish against arbitrary coalitions of the remaining players. The relative value of an individual player is calculated by considering how much he brings to each coalition he might join, that is, by how much the value of that coalition increases because of his membership, and summing this figure over all coalitions of which he could be a part.

Shapley Distance and Shapley Index for Some Special Graphs

2020 ◽  
Vol 30 (04) ◽  
pp. 2050012
Author(s):  
Zhendong Gu ◽  
Shuming Zhou ◽  
Jiafei Liu ◽  
Qianru Zhou ◽  
Dajin Wang
Keyword(s):  
Game Theory ◽  
Shapley Value ◽  
Cooperative Game Theory ◽  
Wiener Index ◽  
Extremal Graphs ◽  
Complete Multipartite Graph ◽  
Kirchhoff Index ◽  
Multipartite Graph ◽  
Complete Multipartite ◽  
The Cost

The Shapley distance in a graph is defined based on Shapley value in cooperative game theory. It is used to measure the cost for a vertex in a graph to access another vertex. In this paper, we establish the Shapley distance between two arbitrary vertices for some special graphs, i.e., path, tree, cycle, complete graph, complete bipartite, and complete multipartite graph. Moreover, based on the Shapley distance, we propose a new index, namely Shapley index, and then compare Shapley index with Wiener index and Kirchhoff index for these special graphs. We also characterize the extremal graphs in which these three indices are equal.

Coalitional Added Services in a Linear Neutral e-Marketplace

2011 ◽  
pp. 33-50
Author(s):  
Paolo Renna ◽  
Pierluigi Argoneto
Keyword(s):  
Game Theory ◽  
Shapley Value ◽  
Profit Sharing ◽  
Related Research ◽  
Planning Activity ◽  
Business Applications ◽  
The Shapley Value ◽  
Auction Mechanisms ◽  
Simulation Results ◽  
Business To Business

The increase of transactions by electronic commerce (e-commerce) in Business to Business applications has a constant trend during last years. Many research reports have focused on negotiation and auction mechanisms in this context, but a smaller number of related research attempts, has chosen to develop coalition approaches This research attempt tries to overcome this gap by an innovative coalition model for a private neutral linear e-marketplace that combines a full integration between customer’s request and supplier’s planning activity. The Shapley value approach is proposed to manage the profit sharing activity among the coalition participants. The Shapley value is an approach of game theory used to share a gain in coalition games. A proper simulation environment has been designed and modeled in order to measure the “stay-together economy” achievable within the proposed innovative e-marketplace. The simulation results highlight how the proposed approach increases the performance level of the e-marketplace: specifically the suppliers gain more benefits than the customers through the possibility of establishing coalitions.

Comparison of Methods for Allocating Costs of Empty Railcar Movements in a Railcar Pooling System

2005 ◽  
Vol 1916 (1) ◽  
pp. 88-95
Author(s):  
Yao Cheng ◽  
Wei-Hua Lin
Keyword(s):  
Game Theory ◽  
Computational Efficiency ◽  
Cost Allocation ◽  
Comparison Of Methods ◽  
Allocation Scheme ◽  
Before And After ◽  
The Cost

Allocating the cost of empty railcar miles to partners in a railcar pooling system is an important pricing problem in railway management. Recently, the authors of this paper proposed a cost allocation scheme for empty railcar movements based on game theory that explicitly considers the level of participation and contribution from each partner, the costs generated before and after cooperation, and the overall benefit obtained by each partner because of cooperation. This paper compares the performance of the model with three other cost allocation models with respect to fairness, stability, and computational efficiency. The comparison is made with two scenarios adapted from examples documented in the literature. The results indicate that the cost allocation scheme based on game theory outperforms other methods in ensuring fairness and enhancing stability in a coalition. Most remarkably, it yields reasonable results even in situations in which other models behave poorly. Computationally, it is manageable for practical problems.

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