A MODEL OF THE EVOLUTION OF DUOPOLY - DOES THE ASYMMETRY BETWEEN FIRMS TEND TO INCREASE OR DECREASE

This paper is an attempt to identify some of the factors that affect t he evolution of market structure in a model of dynamic competition bet ween two firms. The stochastic evolution of the state of competition d epends on the respective effort rates of the firms. The question is wh ether the current leader works harder than the laggard-does the 'gap' between firms tend to increase or decrease? We show that several effec ts are at work. The state tends to evolve in the direction where joint payoffs are greater. Since joint payoffs are related to joint product -market profits less joint effort costs, there are two classes of effe ct: the joint-profit effect and various joint-cost effects. The latter result in part from the pattern of profits, and in part from endpoint effects that give relief from efforts. Asymptotic expansions illumina te these influences. Moreover, we show by numerical simulation that th ere is another kind of joint-cost effect. The pattern of joint effort costs can influence the pattern of evolution of market structure, and the evolution of the pattern of market structure can influence the pat tern of efforts, in a mutually self-reinforcing manner. In particular, there may be equilibria in which this last effect means that the lagg ard works harder than the leader even though all the other effects wor k in favour of the leader.