The Shapley Value As Applied to Cost Allocation: A Reinterpretation

1979 ◽  
Vol 17 (1) ◽  
pp. 295 ◽  
Author(s):  
Alvin E. Roth ◽  
Robert E. Verrecchia
Keyword(s):  
Shapley Value ◽  
Cost Allocation ◽  
The Shapley Value

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.

scholarly journals Shapley Value for Parallel Machine Sequencing Situation without Initial Order

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Shanshan Liu ◽  
Zhaohui Liu
Keyword(s):  
Polynomial Time ◽  
Shapley Value ◽  
Processing Time ◽  
Cost Allocation ◽  
Parallel Machine ◽  
Allocation Rule ◽  
The Shapley Value ◽  
Sequencing Game ◽  
Identical Machine

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.

Cost Allocation with Variable Production and the Shapley Value

2019 ◽  
pp. 200-217
Author(s):  
Miren Josune Albizuri ◽  
Juan Carlos Santos ◽  
José Manuel Zarzuelo
Keyword(s):  
Shapley Value ◽  
Cost Allocation ◽  
The Shapley Value ◽  
Variable Production

scholarly journals UNCERTAINTY OF THE SHAPLEY VALUE

2005 ◽  
Vol 07 (04) ◽  
pp. 517-529 ◽  
Author(s):  
VLADISLAV KARGIN
Keyword(s):  
Shapley Value ◽  
Cost Allocation ◽  
Competitive Equilibrium ◽  
Allocation Problem ◽  
Majority Voting ◽  
Market Games ◽  
Strategic Risk ◽  
The Shapley Value ◽  
Allocation Problems

This paper defines a measure of bargaining uncertainty that quantifies Roth's concept of strategic risk. It shows how this measure can be used for checking reliability of the Shapley value in cost allocation problems and in the theory of competitive equilibrium. Salient properties of the new measure are investigated and illustrated by examples of majority voting and market games and by a cost allocation problem from epidemiology.

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.

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.

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