A game theoretic approach to coordination of pricing, ordering, and co-op advertising in supply chains with stochastic demand

Abstract

The present study aims to investigate the combination of the newsboy problem and the cooperative advertisement problem in the presence of uncertain demand which depends on retail price as well as both local and national advertising expenditures to coordinate pricing, ordering, and advertising decisions in a manufacturer-retailer supply chain. A game theoretic approach was adopted to determine the equilibrium values for decisions. Three different game scenarios based on the newsboy problem model were developed and analyzed: 1) Stackelberg manufacturer game in which the manufacturer as the dominant power plays the role of leader in the market and the follower retailer makes his own best decisions after considering the leader's decisions; 2) Nash equilibrium game in which both manufacturer and retailer are of equal power in the market and make their decisions simultaneously to devise their best strategies; 3) Centralized scenario in which the retailer and manufacturer make the best decisions by means of information sharing and joint cooperation. Equilibrium decisions were made exactly in these scenarios. Some corollaries were also presented and theoretically proved to show the relationships among the variables in both centralized and decentralized supply chains. Finally, some numerical examples were randomly generated and sensitivity analysis was carried out to show the capabilities of the proposed models.