Modelling effects of correlation in price competition

Abstract

Firms try to sell their products or services with a predetermined scheme to earn the most profit possible. For this, they first should know the demand characteristics of their product or service. Commonly, the market structure of a product or service is not a monopoly, that is, there are several firms competing on the sale of a typical product or service. In such environments, it is possible that customers decide on their choice considering the whole market instead of focusing on a particular firm. Having this in mind, one should consider the correlation between the demands of different firms’ product or services to better analyze the system. In this study, we examine a price competition under the assumption of a simple demand model which utilizes willingness to pay distributions of the customers in the market. The model allows that the demands of the firms may be correlated. This way, the demand model takes into account the dependencies between the firms’ services. We present the characteristics of the model and the equilibrium behavior of the competition. After, we investigate the dynamics of the competition under the assumption of Gumbel’s bivariate exponential distribution (so-called Gumbel’s Type 2) for the demands for the firms. We prove the existence of a unique Nash equilibrium for the price decisions of the firms. It turns out that under certain conditions, the equilibrium price of the firms may be higher than the monopoly case optimum price. Besides, some comparative statics for centralization and decentralization are presented. Numerical examples are presented for different cases.