Pricing in a duopoly market using a representative consumer model - Moo, Zi Hao (Nanyang Technological University, 2023)
In this report, we develop an approach for the pricing problem in a duopoly market, using a representative consumer model. We establish mathematical relationships between product prices and demand for each product, including the product of the competing firm and also the outside option. More precisely, we include a perturbation function in the optimization problem of consumer’s valuation, and use it to obtain the optimal pricing of each product. Using piecewise linear approximation, we show that the resulting problem can be solved as mixed integer linear programs. Pricing experiments in different settings were done to compare the performance of our methods to the well-established MIP model. The results show that although our approach performs badly in some of the settings (more precisely, when the competing firms have products with higher mean or variance of valuations), it performs close to the level of MIP in the other settings, and it is much more computationally efficient. We also find out the reason our approach performs badly in some of the settings, which is due to the uneven distribution of breakpoints, which can cause higher error in piecewise linear approximation.