N-Person Dynamic Oligopoly : The Case of Conjectured Price Variations Under Certainty

This paper derives the dynamic implications for price setting in an Edgeworth oligoppoly game with N>2 competitors. The impetus to the dynamic game are "conjectured" variations in the prices set by competing firms whereby each firm expresses its belief that a decrease in its own price will be met by not necessarily matching price decreases by its opponents, but that an increase in its price will not be matched, where the demand function for each seller is a decreasing function of its price and an increasing function of those of all the others. The Hamiltonian derived from each oligopolist solving the present value of a stream of profits that depend on its own price and those of its competitors produces a set of interrelated simultaneous Euler equations and decision rules whose existence is proved. The existence of a time-varying saddle point allows expressing the industry solution for prices as a matrix flexible accelerator familiar in investment theory, where prices adjust slowly to approach the moving steady state path formed by (expected) forward histories of prices, also known as a turnpike