Consider G = (X1,â¦,XM,g1,â¦,gM) an M-player game in strategic form, where the set Xi is an interval of real numbers and the payoff functions gi are differentiable with respect to the related variable xi â Xi. If they are also concave, with respect to the related variable, then it is possible to associate to the game G a variational inequality which characterizes its Nash equilibrium points. In this paper it is considered the variational inequality for two sets of Cournot oligopoly games. In the first case, for any i = 1,â¦,M, we have Xi = [0,+â); the market price function is in C1 and convex; the cost production function of the player i is linear and the function xi â gi(â¦,xi,â¦) is strictly concave. We prove the existence and uniqueness of the Nash equilibrium point and illustrate, with an example, an algorithm which calculates its components. In the second case, for any i = 1,â¦,M, we have Xi = [0,+â); the market price function is in C2 and concave and the cost production function of the i-player is in C2 and convex. In these circumstances, as a consequence of well known facts, the existence and uniqueness of the Nash equilibrium point are guaranteed and also the Tykhonov and Hadamard well-posedness of the game. We prove that the game G is well posed with respect to its variational inequality.
Non co-operative games, Cournot oligopoly, Nash equilibria, variational inequalities, well-posedness
In order to set up a list of libraries that you have access to,
you must first login
or sign up.
Then set up a personal list of libraries from your profile page by
clicking on your user name at the top right of any screen.