Chaos in Duopoly Pricing

The dynamics of two competing firms in a market is studied in terms of Cournot's duopoly theory. Assuming iso-elastic demand and constant unit production costs the iterative mapping x(1)=root y(1-1)/a-y(1-1), y(1)=root x(1-1)/b-x(1-1) for the outputs of the two firms ensues. The two constants are the unit production costs. The fixed point, the Cournot equilibrium, has earlier been assumed to be the only interesting feature of this model. It is, however, shown that the model can produce persistent motion, periodic or chaotic.