Game-theoretic analysis of coordinating pricing and marketing decisions in a multi-product multi-echelon supply chain

Supply chain coordination aims at improving supply chain performance by aligning the decisions and the objectives of individual firms. Supply chain participants can coordinate on different decisions such as pricing, inventory management, and marketing decisions to gain more profit. The current research considers coordination of these decisions in a multi-product multi-echelon supply chain composed of multiple suppliers, single manufacturer, and multiple retailers. It is assumed that the demand of each product is non-linearly influenced by retailing price and marketing expenditure. Since all the supply chain members possess equal power in the market and make their decisions simultaneously, the three echelon supply chain problem is a non-cooperative Nash game. In order to find the Nash equilibrium, we formulate a Non-linear Complementarity Problem (NCP) based on the optimality conditions, and also an iterative algorithm is proposed to solve large size instances. Finally, a numerical example is presented, and a comprehensive sensitivity analysis is conducted to discuss important managerial insights.