A Dynamic Approach to Oligopolistic Market Equilibrium

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