Biform game analysis with the Owen allocation function for a supply chain game under precedence constraints

Supply chain operational management is a challenging yet critical task owing to the supply chain’s complex structure. For example, the flow of material information establishes diverse ordered relationships among members. At the same time, suppliers, manufacturers, wholesalers, and others collaboratively make decisions on multiple fronts, which may result in a situation where a member belongs to various coalitions. This complex supply chain operational management can be coordinated by members implementing reasonable and efficient joint competitive strategies within the ordered relationship. To address the operational management challenges posed by these intricate relationships, we construct a coalition structure by introducing the precedence constraints. Based on this structure, we propose a biform game mechanism that integrates non-cooperative and cooperative games to harmonize the joint competitive strategies of members. This mechanism can model the precedence relationships of member and asset flow, derive a Nash equilibrium for joint independent investment, and provide an efficient allocation scheme based on an extended Owen value. Moreover, through numerical analysis, we illustrate the influence of precedence constraints on this mechanism. Our findings contribute to the ongoing operational management on the role of member relationships in enhancing supply chain performance by developing a novel biform game in which the cooperation stage is modeled as a cooperative game with precedence-constrained coalition intersections.