A Biform Game Model with the Shapley Allocation Functions

We define the mixed strategy form of the characteristic function of the biform games and build the Shapley allocation function (SAF) on each mixed strategy profile in the second stage of the biform games. SAF provides a more detailed and accurate picture of the fairness of the strategic contribution and reflects the degree of the players’ further choices of strategies. SAF can guarantee the existence of Nash equilibrium in the first stage of the non-cooperative games. The existence and uniqueness of SAF on each mixed strategy profile overcome the defect that the core may be an empty set and provide a fair allocation method when the core element is not unique. Moreover, SAF can be used as an important reference or substitute for the core with the confidence index.

Modeling the Design Phase of Sustainable Supply Chains

The objective of supply chain sustainability is to create, protect, and grow long-term environmental, social, and economic value for all stakeholders involved in bringing products and services to market. This chapter creates a comprehensive model and solution methods for designing sustainable supply chains. Sustainable supply chains are modeled as network systems with multiple agents, which are evaluated according to multiple criteria. It is usually impossible to optimize all criteria together in a given system. Searching for a better portfolio of resources leads to reshaping of given system boundaries and better criteria values. Supply chain sustainability is also given by creating equilibrium relationships between agents. Biform games are used for searching an equilibrium in sustainable supply chains. Information sharing reduces inefficiencies and material flows, leading to less environmental pollution.