A mathematical model on sequential discount transfer in a three-level channel

Abstract

Although there are some game-theoretic price discount models, three-level game-theoretic sequential price discount models have not been considered. This work considers a manufacturer-distributor-retailer channel on price discount using game theory. The manufacturer is considered to be the channel leader; the distributor is the first follower, while the retailer is the second follower. It considers a situation where the manufacturer gives price discount to the distributor, who in-turn is expected to also provide price discount to the consumer. The work models the players’ payoffs using balance equations involving price, discount rate and linear demand function. The work considers four scenarios: neither of the players gives discount; only one player gives discount; two players give discount; and all-three players give discount. For each scenario the work obtained the prices and payoffs of each player. It shows that giving of discount reduces a player’s payoff, and that instead of all the players engaging in price discount, a player can do that for the entire channel. However, a sharing formula must be reached to ensure that the player that provides the discount is not short-changed.