The article is concerned with market behavior when firms have limited ability to handle effectively the complexity of changing market conditions and strategic interaction . Modelling the managerial bounded rationality by using the concept of strategic complexity as measured by a finite automation, we show that market behavior can be considerably altered once there is a limit on the complexity of strategies. In particular, we demonstrate that when an incumbent firm operates in several markets, an entry to one market may induce the incumbent to exit from another market (divestiture) in order to "concentrate" on the competition it faces. For different parameters the incumbent may react to such an entry by exit from the same market, creating specialization. We also demonstrate that bounded complexity can serve as an entry barrier, giving an advantage to the established incumbent firm.