Shapley Value: its algorithms and application to supply chains

Abstract

Introduction: Coalitional game theorists have studied the coalition structure and the payoff schemes attributed to such coalition. With respect to the payoff value, there are number ways of obtaining to “best” distribution of the value of the game. The solution concept or payoff value distribution that is canonically held to fairly dividing a coalition’s value is called the Shapley Value. It is probably the most important regulatory payoff scheme in coalition games. The reason the Shapley value has been the focus of so much interest is that it represents a distinct approach to the problems of complex strategic interaction that game theory tries to solve. Objective: This study aims to do a brief literature review of the application of Shapley Value for solving problems in different cooperation fields and the importance of studying existing methods to facilitate their calculation. This review is focused on the algorithmic view of cooperative game theory with a special emphasis on supply chains. Additionally, an algorithm for the calculation of the Shapley Value is proposed and numerical examples are used in order to validate the proposed algorithm. Methodology: First of all, the algorithms used to calculate Shapley value were identified. The element forming a supply chain were also identified. The cooperation between the members of the supply chain ways is simulated and the Shapley Value is calculated using the proposed algorithm in order to check its applicability. Results and Conclusions: The algorithmic approach introduced in this paper does not wish to belittle the contributions made so far but intends to provide a straightforward solution for decision problems that involve supply chains. An efficient and feasible way of calculating the Shapley Value when player structures are known beforehand provides the advantage of reducing the amount of effort in calculating all possible coalition structures prior to the Shapley.

Keywords

• Cooperative games
• Shapley value
• Supply chain
• competitiveness
• cluster