In this thesis the equilibrium behavior of a price competition model under Logit choice model is studied. In recent decades price competition games under discrete choice models have been wildly studied by researchers. To our knowledge, in these models the number of sold items for a product is assumed to be equal to demand for that product and as a result the costs related to the inventory including overage and underage costs are not considered. In this study, with deriving a random demand function from Logit choice model, two single period random models in a competitive market are proposed. In the first model, the retailers have an intermediate role and do not decide about the price or order quantity. In this model it is assumed that, the retailers convey the demand from customers to suppliers without any change. The suppliers would encounter with shortage or surplus of products depending on the number of products produced by them.The goal of this model is to determine the price and the quantity to be produced for maximizing the profit. In this model the routing cost are also considered using an approximate equation. Due to the computational complexity of finding the Nash equilibrium in the proposed game, an approximate method is proposed. The results show the high accuracy of the proposed approximate method, moreover this method spends time much less than the main model for finding the equilibrium. In the second model it is assumed that the retailers would be encountered with overage and underage costsdepending on the number of products ordered by them. In this model, like the first model, the prices are determined by suppliers and the decision variables for retailers are order quantities. As one the most important works in this thesis, the existence of Nash equilibrium is proved in this model which is always one of the most important and also complicated aspects of the games.