Study of price and assortment competition in retail

Abstract

[en] In this work we study the competition between two retailers that have to choose which of the available products to sell and at which price, knowing that each customer relates a product and its price with a value and will only acquire the product with highest value. In the first part of this project we present our framework by defining some of the basic concepts of Game Theory and introducing new terminology. Moreover, we also review two of the pioneering models in duopolistic competition: the Cournot and Bertrand model. The second part of the project formally defines and models the competitive situation. We formally establish the actions available for both retailers and determine how each customer ranks all products for sale. Moreover, in this chapter we also study the effects that this competition has, the possible equilibria of this competitive market and under which circumstances both retailers can reach such equilibria. The third part of the project further studies the relationship between the price a retailer sets for his products and whether the product is common or exclusive. We attempt to model this relationship with a linear regression model and we study the results with data from clothing retailers Gucci and Farfetch.