Developing an All-Unit Quantity Discount Model with Complete and Incomplete Information: A Bertrand Competition Framework

There are studies regarding monopolistic all-unit quantity discount but we add the duopoly Bertrand competition under incomplete information with it, which is not treated earlier. Then, a systematic procedure is outlined to compute pay-off functions for the developed game. A real numerical example is given in support of the solution procedure and a sensitivity analysis is carried out to examine the important parameters on the equilibrium quantities. This study provides several interesting insights. For instance, it is approved that if retailers know each other completely or not, under some special conditions, rejecting the offered discount is the strictly dominant strategy adopted by the retailers. By doing sensitivity analysis for a real-world case, it is displayed that for maximizing profit, the company should pay more attention to increasing the demand rather than reducing the costs. It could be seen that a change in the value of all parameters except the fixed ordering cost and the holding cost rate results in changing the discount strategy selected by the retailers. Investigating an incomplete information in comparison with the common knowledge case, it is necessary that retailers obtain more accurate knowledge about their rivals.