Università degli Studi di Genova
The authors consider a mathematical model in which a Cournot oligopoly is represented as a game in normal (strategic) form. Their main purpose is to find sufficient conditions to assure the existence of Nash equilibria for this game (and even more, to assure uniqueness of the equilibrium under a certain continuous dependence on the data). Relating the existence of a Nash equilibrium in such a situation with the existence of a solution to a variational inequality generated by the (differentiable) payoff functions, the authors prove the above existence and uniqueness of the Nash equilibrium in the following two cases: in the first case the price function is convex and continuously differentiable, the cost functions are linear and a standard concavity assumption is made for the payoff functions; the second case is when the price function is concave and both the price function and the cost functions are twice continuously differentiable. In addition to the first existence result, an algorithm that obtains the unique Nash equilibrium point is proposed.
Non co-operative games; Cournot oligopoly; Nash equilibria; variational inequalities; well-posedness
Pubblicato su International Game Theory Review 9(2007) n.4 pp.583-598
Pubblicato su: International Game Theory Review Vol. 9 (2007) Pag. 583-598