Nearly-complete Decomposability and Stochastic Stability with an Application to Cournot Oligopoly

This paper presents a general framework for analysing stochastic stability in models with evolution at two levels. Under certain conditions the theory of nearly-complete decomposability can be used to disentangle these two levels. They can then be studied separately and the equilibrium of one can be used to obtain the equilibrium of the other. This gives an approximation of the equi- librium of the combined dynamics. This approached is applied to a model of conjectural variation and imitation in Cournot oligopoly. If behavioural change takes place infrequently, the Walrasian equilibrium is the unique stochastically stable outcome. As a corollary, it is indicated that smaller industries are more competitive than larger ones.