This study investigates the optimal strategies of a monopoly platform with two distinct sides by building a simple model on two-sided market with the essence of cross-group network externality. The platform provides discount to its buyers. One of the significant innovations of our model lies in the fact that discount not only provides monetary benefit of paying less to purchase the discounted product, but it also adds to psychological utility of buyers. Further, we assume that the monopoly platform, in particular, uses advertising signals to spread discount information among buyers and also provides services to buyers. We then find the profit maximising level of prices charged to both groups, service quality and the level of advertisement sent by the platform. We observe that although discount adds benefit to buyers’ utilities only, it influences the prices charged to both buyers and sellers because of the existence of indirect network externality. Sensitivity analysis has been performed and it shows that both, service quality and the level of advertisement, will fall unambiguously with discount for a monopoly platform. As a result, the volume of transaction also reduces with increase in discount. Thus, offering a large discount is not always desirable as it may negatively affect the service performance of the platform in the long term and that will lead to fall in volume of purchase, particularly for the quality conscious buyers. Executives of businesses should keep all these effects in mind before devising any discount strategy. On comparing monopoly equilibrium and social optimum, we find that monopoly platform sets higher service quality compared to social welfare case. Numerical analysis has also been conducted for certain parameter values to validate the analytical findings.