A Model of the Evolution of Duopoly: Does the Asymmetry between Firms Tend to Increase or Decrease?

The stochastic evolution of competition depends on the respective effort rates of the firms. We show that several effects 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 effect: 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. There is another kind of joint-cost effect which we identify. There may be equilibria in which this last effect means that the laggard works harder than the leader even though all the other effects work in favor of the leader.