This paper examines a competition in both quality and quantity between two asymmetric restaurants. The model that we consider is a Stackelberg duopoly on quantities (sequential decision-making), after a simultaneous choice of quality. Our findings indicate that the restaurant with the best reputation provides a greater variety of higher-quality food compared to its competitor. We also examine how variations in restaurants’ reputations impact market equilibrium outcomes. We demonstrate that an increase in the reputation gap between restaurants boosts the profits of both establishments, enhances consumer surplus, and improves social welfare. Additionally, in comparison to the scenario under the Cournot model (simultaneous decision-making), small restaurant’s profits are lower under Stackelberg model, while the opposite holds for the large restaurant’s profits and for social welfare.