This paper deals with a situation of middle-man behavior between two otherwise separated economies. A two-person noncooperative exchange game is proposed whereby each player's strategy consists of two parts taken in a sequence: a price strategy, to be followed by a demand strategy. The concept of a special kind of mixed strategies is introduced, and a solution is defined in terms of a Nash equilibrium pair of such mixed strategies. It is shown that a trivial class of equilibria always exists, and that under certain conditions, more interesting nontrivial equilibria can exist as well.