Two large paper mills dominate the forest industry in northern Iran. Forest companies and local farmers sell pulpwood to these mills. The real pulpwood price data was collected from two paper mills in the northern part of Iran. These mills buy most pulpwood in this area. Game theory has been used in order to investigate the market structure in this region. Game theory is the study of interacting decision makers. Game theory has been widely used in economics. Most economic behaviour can be viewed as a special case of game theory. A game model includes a set of players, a set of strategies and a set of payoffs. This study focuses on the theory of dynamic duopsony games. When pulpwood is sold, the different mills use mixed strategies to give sealed bids. In each transaction, each mill (player) has two different possible strategies (decisions): a high (H) or a low (L) prices. Which price should you set? What is the optimal price of the other player? Here the situation is a noncooperative game. Nash equilibrium and dynamic properties of the system are determined. Each mill continuously observes the frequencies of the other mills action. The expected marginal profits are calculated based on this information. In case the marginal profit of mill A is strictly positive (zero or strictly negative), mill A increases (leaves unchanged, decreases) bids. In case the marginal profit of mill B is strictly positive (zero or strictly negative), mill B increases (leaves unchanged, decreases) 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.