Generalized quantity competition for multiple products and loss of efficiency

In this paper we study a generalized model for quantity (Cournot) oligopolistic competition. The main goal in this paper is to understand Cournot competition when firms are producing multiple differentiated products and are faced with a variety of constraints. We first study existence and uniqueness of Cournot equilibria under general constraints. The main focus of the paper is to compare the total society surplus and the total firms' profit under Cournot competition to the corresponding total surplus and total profit of the firms under a centralized setting, (i.e., when a single firm controls all the products in the market maximizing total surplus or total profit respectively). Our goal is to understand how the presence of competition affects the overall society (that includes firms and consumers) as well as the overall firms' profit in the system, but also determine what the key drivers of the inefficiencies that arise due to competition are.