An all-unit quantity discount model under a Cournot competition with incomplete information

The economic order quantity model is a fundamental model in inventory control that introduces retailer's optimal strategy under some conditions such as the unit cost of purchased product is constant and also the retailer and the supplier work in a monopolistic market and the effects of the behaviors of their competitors on their demand are ignored but in the real world, these conditions are hard to encounter. This research studies an all-unit quantity discount model in an oligopolistic retailing market and finds the best lot size of each retailer for the both cases in which the inventory cost structure of retailers are common knowledge and are not. The obtained results show that rejecting discount by two retailers is Nash equilibrium in the former case. Finally, applicability of the proposed models is shown by solving a real numerical example.