The objective of this dissertation is show that even in environments where the decision of the individual not follow rationality, we can get a optimal strategy. with the help of evolutionarily stable strategy, we analyze different cases of the usual literature on game theory that even with choices without rationality, we find the best strategy, for that we will use the option game methodology, which is the union between gaming theory methodology and option game methodology, with the concept of evolutionarily stable strategy (ESS). This is demonstrated through modeling of a duopolistic market, with uncertainties, in this dissertation firms are different. Here companies has no-Homogeneous cost because a company has lower operating costs than the other for the same investment. This means that a company has competitive advantage over rival. The model results show that, depending on the strategy assumed by the company it is possible that the low-cost company to become leader as usual in the literature and in some cases also shows that is possible to the high cost company to become leader and demonstrates that the premise of rationality are not necessary for choosing initial strategy, the company can find equilibrium using the concept of ESS to set the balance as was done in the paper of Xiao and YU (2006).