Some Methods for the Global Analysis of Dynamic Games Represented by Iterated Noninvertible Maps

The time evolution of an oligopoly system is often described as an n-players game which is played repeatedly, in the sense that at each discrete time period t = 0, 1,..., n producers choose their actions, x₁(t), ... ,x _n (t), by solving an optimization problem based on the knowledge of the actions observed in the past. For example, the classical Cournot adjustment (see Cournot, 1838, Teocharis, 1960, and many others) is obtained by assuming that at each period any player chooses its own production strategy which is a best response to the choices of the competitors in the previous period.