Nash Equilibrium In A Duopoly Market With Learning Effects

We modify the Cournot model by allowing for two production periods under the duopoly market environment. The firms choose retail prices and outputs simultaneous-ly in the two periods. Each firm makes their decision independently while aware of both their own and competitor’s demand functions of the customers. Unit cost for each item they manufacture in the second period is a decreasing linear function of the pro-duction quantity in the first period. The goal for each firm is to optimize its profit for two periods. We solve the problem by coming up with the Nash equilibrium solution; therefore; giving the optimal price, optimal quantity for each firm in each period.In the extended model, we consider these two firms ordering raw materials from two suppliers then assemble and sell the products to customers. Each supplier takes an order from both firms and in the second period, each supplier’s unit cost decreases as the amount they sell in the first period increases. The cost therefore has an impact on the suppliers’wholesale price which would influence the manufacturers’ ordering decisions. Therefore, we manage to take a look at the influence of each firm’s choice on their competitor.