Title: Shapley value and other allocation schemes for three-person supply chain games

Authors: Xu Zhang; Panlop Zeephongsekul

Addresses: School of Mathematical and Geospatial Sciences, RMIT University, GPO Box 2476V, Melbourne, VIC 3001, Australia ' School of Mathematical and Geospatial Sciences, RMIT University, GPO Box 2476V, Melbourne, VIC 3001, Australia

Abstract: A game theoretical approach to modelling different supply chains has become a very active area of research in supply chain management during the last two decades. The models that are currently used employed both a non-cooperative and a cooperative approach. Most studies also concentrate on upstream members of the supply chain and ignore the contribution of the consumer downstream and her influence on decisions made by the other members of the chain. In this paper, the consumer, whose purchasing decision would affect the strategies adopted by other players, is an active member of the three-person supply chain games. We present several supply chain models involving a supplier, a retailer and a consumer under both a non-cooperative and cooperative game scenario. Nash equilibrium solutions will be obtained for players in the non-cooperative game, and Pareto and Shapley values in the cooperative game. Numerical examples illustrating and comparing between the different models are also provided.

Keywords: three-person supply chain games; Nash equilibrium; Shapley value; Pareto optimum; coalitional games; allocation schemes; game theory; supply chain modelling; supply chain management; SCM; consumer involvement; purchasing decisions.

DOI: 10.1504/IJIR.2015.073946

International Journal of Inventory Research, 2015 Vol.2 No.4, pp.264 - 288

Received: 01 Aug 2015
Accepted: 15 Aug 2015
Published online: 30 Dec 2015 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article