Analysis of equilibrium for multi-retailer price competition based on supermodular game theory

The equilibrium behavior was studied in the context of a two-echelon supply chain with one supplier and many price-competing retailers. Retailers played a price game under price-dependent stochastic demand and revenue-sharing contracts. Based on the theory of supermodular games, existence of pure strategy Nash equilibrium was proved, characteristics of the equilibrium were analyzed, and the existing conditions of unique equilibrium were also presented. In addition, by static comparison, the change rule of equilibrium price along with the change of the parameters were summarized. Finally, accuracy of the results was verified by a numerical example.