A game theoretic approach to pricing, advertising and collection decisions’ adjustment in a closed-loop supply chain

This paper considers advertising, collection and pricing decisions simultaneously for a closed-loop supply chain (CLSC) with one manufacturer (he) and two retailers (she). A multiplicatively separable new demand function is proposed which influenced by pricing and advertising. In this paper, three well-known scenarios in the game theory including the Nash, Stackelberg and Cooperative games are exploited to study the effects of pricing, advertising and collection decisions on the CLSC. Using these scenarios, we identify optimal decisions in each case for the manufacture and retailers. Extending the Manufacturer-Stackelberg scenario, we introduce the manufacturer’s risk-averse behavior in a leader–follower type move under asymmetric information, focusing specifically on how the riskaverse behavior of the manufacturer influences all of the optimal decisions and construct manufacturer-Stackelberg games in which each retailer has more information regarding the market size than the manufacturer and another retailer. Under the mean–variance decision framework, we develop a closed-loop supply chain model and obtain the optimal equilibrium results. In the situation of the stackelberg game, we find that whether utility of the manufacturer is better off or worse off depends on the manufacturer’s return rate and the degree of risk aversion under asymmetric and symmetric information structures. Numerical experiments compare the outcomes of decisions and profits among the mentioned games in order to study the application of the models.