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Variational Inequalities In Cournot Oligopoly

Listed author(s):


    (Department of Mathematics and Physics, University of Sassari, Via Vienna 2, 07100 Sassari, Italy, IT, Italy)

  • G. PIERI


    (D.S.A., University of Genoa, Stradone S. Agostino 37, 16136 Genova, Italy, IT, Italy)

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    Consider G = (X1,…,XM,g1,…,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 ∈ 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,…,M, we have Xi = [0,+∞); the market price function is in C1 and convex; the cost production function of the player i is linear and the function xi → gi(…,xi,…) 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,…,M, we have Xi = [0,+∞); 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.

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    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Game Theory Review.

    Volume (Year): 09 (2007)
    Issue (Month): 04 ()
    Pages: 583-598

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    Handle: RePEc:wsi:igtrxx:v:09:y:2007:i:04:p:583-598
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