Imitation by price and quantity setting firms in a differentiated market

We study the evolution of imitation behaviour in a differentiated market where firms are located equidistantly on a (Salop) circle. Firms choose price and quantity simultaneously, leaving open the possibility for non-market-clearing outcomes. The strategy of the most successful firm is imitated. Behaviour in the stochastically stable outcome depends on the level of market differentiation and corresponds exactly with the Nash equilibrium outcome of the underlying stage game. For high level of differentiation, firms end up at the monopoly outcome. For intermediate level of differentiation, they gravitate to a “mutually non-aggressive” outcome where price is higher than the monopoly price. For low level of differentiation, firms price at a mark-up above the marginal cost. Market-clearing always results endogenously.