A Continuous Approach to Oligopolistic Market Equilibrium

We provide an algorithm for computing Cournot-Nash equilibria in a market that involves finitely many producers. The algorithm amounts to following a certain dynamical system all the way to its steady state, which happens to be a noncooperative equilibrium. The dynamics arise quite naturally as follows. Let each producer continuously adjust the planned production, if desired, as a response to the current aggregate supply. In doing so, the producer is completely guided by myopic profit considerations. We show, under broad hypothesis, that this adjustment process is globally, asymptotically convergent to a Nash equilibrium.

[1]  G. Debreu.  Existence of competitive equilibrium , 1982 .

[2]  Naum Zuselevich Shor,et al.  Minimization Methods for Non-Differentiable Functions , 1985, Springer Series in Computational Mathematics.

[3]  George A Kondor.  On the asymptotic local stability of autonomous economic systems with nonnegativity conditions , 1981 .

[4]  Patrick T. Harker,et al.  Alternative Models of Spatial Competition , 1986, Oper. Res..

[5]  Jesús Seade.  THE STABILITY OF COURNOT REVISITED , 1980 .

[6]  Anna Nagurney,et al.  A general dynamic spatial price equilibrium model: formulation, solution, and computational results , 1988 .

[7]  M. S. Bazaraa,et al.  Nonlinear Programming , 1979 .

[8]  A. Nagurney,et al.  A network formulation of market equilibrium problems and variational inequalities , 1984 .

[9]  Ken Binmore,et al.  A game-theoretic approach to political economy , 1984 .

[10]  Stella Dafermos,et al.  An iterative scheme for variational inequalities , 1983, Math. Program..

[11]  Patrice Marcotte.  Quelques notes et résultats nouveaux sur le problème d'équilibre d'un oligopole , 1984 .

[12]  J. Aubin,et al.  L'analyse non linéaire et ses motivations économiques , 1984 .

[13]  Patrick T. Harker,et al.  A variational inequality approach for the determination of oligopolistic market equilibrium , 1984, Math. Program..

[14]  S. Dafermos.  Relaxation Algorithms for the General Asymmetric Traffic Equilibrium Problem , 1982 .

[15]  Vladimir Igorevich Arnolʹd,et al.  Équations différentielles ordinaires , 1974 .

[16]  S. Karamardian.  Generalized complementarity problem , 1970 .

[17]  W. Novshek.  On the Existence of Cournot Equilibrium , 1985 .

[18]  C. B. García,et al.  Equilibrium programming:The path following approach and dynamics , 1981, Math. Program..

[19]  A. Auslender.  Optimisation : méthodes numériques , 1976 .

[20]  D. Kinderlehrer,et al.  An introduction to variational inequalities and their applications , 1980 .

[21]  Hanif D. Sherali,et al.  A mathematical programming approach for determining oligopolistic market equilibrium , 1982, Math. Program..

[22]  C. Henry.  Differential equations with discontinuous right-hand side for planning procedures , 1972 .

[23]  S. Yakowitz,et al.  A New Proof of the Existence and Uniqueness of the Cournot Equilibrium , 1977 .

[24]  J. Drèze,et al.  Stability theorems with economic applications , 1977 .

[25]  Stella Dafermos,et al.  Traffic Equilibrium and Variational Inequalities , 1980 .

[26]  Jong-Shi Pang,et al.  Iterative methods for variational and complementarity problems , 1982, Math. Program..

[27]  J. Goodman.  Note on Existence and Uniqueness of Equilibrium Points for Concave N-Person Games , 1965 .

[28]  Hugo Sonnenschein,et al.  On the existence of Cournot equilbrium without concave profit functions , 1976 .