Dynamic game theory is applied to analyze the timber market in northern Iran as a duopsony. The Nash equilibrium and the dynamic properties of the system based on marginal adjustments are determined. When timber is sold, the different mills use mixed strategies to give sealed bids. It is found that the decision probability combination of the different mills follow a special form of attractor and that centers should be expected to appear in unconstrained games. Since the probabilities of different strategies are always found in the interval [0,1], the boundaries of the feasible set are sometimes binding constraints. Then, the attractor becomes a constrained probability orbit. In the studied game, the probability that the Nash equilibrium will be reached is almost zero. The dynamic properties of timber prices derived via the duopsony game model are found also in the real empirical price series from the north of Iran.