English, Article edition: VARIATIONAL INEQUALITIES IN COURNOT OLIGOPOLY C. A. PENSAVALLE; G. PIERI

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Physical Description
  • article
Language
  • English

Edition details

Title
  • VARIATIONAL INEQUALITIES IN COURNOT OLIGOPOLY
Author
  • C. A. PENSAVALLE
  • G. PIERI
Physical Description
  • article
Notes
  • 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
  • RePEc:wsi:igtrxx:v:09:y:2007:i:04:p:583-598
Language
  • English
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