Winning in Retail Market Games: Relative Profit and Logit Demand

We examine retailers that maximize their relative profit, which is the (absolute) profit relative to the average profit of the other retailers. Customer behavior is modelled by a multinomial logit (MNL) demand model. Although retailers with low retail prices attract more customers than retailers with high retail prices, the retailer with the lowest retail price, according to this model, does not attract all the customers. We provide first and second order derivatives, and show that the relative profit, as a function of the retailer's own price, has a unique local maximum. Our experiments show that relative profit maximizers "beat" absolute profit maximizers, i.e. they outperform absolute profit maximizers if the goal is to make a higher profit. These results provide insight into market simulation competitions, such as the Power TAC.