Comparative advertising is a type of advertising in which a brand attempts to disparage other brands by name, illustration, or other distinguishing characteristics to increase its market share. We consider a scenario in which a brand manager creates an ad strategy for a firm and must determine which advertising campaign (comparative advertisements (CA) or non-comparative advertisements (NCA)) to pursue. We first solve a monopolistic case where a brand optimizes its market share without considering rivals based on market and consumer conditions. However, in the real world, this decision cannot be taken unilaterally, as the rival brand’s strategy will affect the brand’s market share. Therefore, we propose a dynamic stochastic model of advertising competition in which brands repeatedly advertise, compete in the product market, and make advertising decisions. In our research, we solve a two-player dynamic stochastic game with discrete time, discrete state, and an infinite time horizon. We develop and illustrate a simple algorithm for computing Markov-perfect equilibrium(MPE). We conclude that as consumer skepticism and susceptibility to manipulation increase, our algorithm suggests choosing MPE ad strategy CA less frequently when the manipulative intent of comparative advertising is heightened, while keeping the information availability of ads constant. Conversely, when consumers are less easily manipulated, increasing the manipulative intent of comparative advertising leads to a higher frequency of CA. Additionally, increasing the information availability of ads while keeping manipulation constant results in a higher frequency of CA for non-skeptical customers compared to skeptical customers. In summary, customer skepticism, information availability, and manipulative intent influence both players’ Markov perfect equilibrium ad strategy.