A Continuous Approach to Oligopolistic Market Equilibrium

Sjur Didrik Flåm · Adi Ben-Israel

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Game Theory and Applications Merger and Competition Analysis Economic theories and models

Abstract

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.

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References

1965Existence and Uniqueness of Equilibrium Points for Concave N-Person Games 1980Traffic Equilibrium and Variational Inequalities 1985On the Existence of Cournot Equilibrium 1982A mathematical programming approach for determining oligopolistic market equilibrium 1980The stability of cournot revisited 1977A New Proof of the Existence and Uniqueness of the Cournot Equilibrium 1986Alternative Models of Spatial Competition 1986A Game Theoretic Approach to Political Economy.

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