Imperfect competition in markets can lead to different outcomes for consumers. The Cournot and Bertrand models are commonly used to study this. A mix of these two models is also gaining interest. In a duopoly market with product differentiation, one firm using Cournot behavior and the other using Bertrand behavior can both survive if there is enough differentiation. If products are very similar, the market can become unstable. In a scenario with identical products, the Cournot-type firm will produce at a competitive level and the Bertrand-type will exit. This shows the importance of product differences in market stability. The study also looks at Nash equilibrium, stability, and the impact of product differences on market survival. Simulation results show how prices, quantities, and profits change with different model parameters.