Today, many companies take advantage of viral marketing to promote their new products, and since there are several competing companies in many markets, Competitive Influence Maximization has attracted much attention. Two categories of studies exist in the literature. First, studies that analyze the problem of which nodes from the network to select considering the existence of the opponents. Second, studies that focus on the problem of budget allocation. Although these studies have improved the problem in many aspects, their considered scenario is still incomplete. In this paper, we integrate these two lines of researches and propose a much more realistic scenario for the Competitive Influence Maximization problem. In our scenario, competition happens in two phases. First, parties identify the most influential nodes of the network. Then they compete over only these influential nodes by the amount of budget they allocate to each node. Also, despite the common assumption in all previous budget allocation studies that the action space is continuous, we consider the action space to be discrete. This assumption is more connected to real-world applications and significantly changes the problem. We model the scenario as a game and propose a novel framework for calculating the Nash equilibrium. Notably, building an efficient framework for this problem with such a huge action space and also handling the stochastic environment of influence maximization is very challenging. To tackle these difficulties, we devise a new payoff estimation method and a novel best response oracle to boost the efficiency of our framework.