Improper disposal of household unwanted medications (UMs) is an emergency problem around the world that adversely affects the sustainability of the environment and human’s health. However, the current disposal practices, mainly based on advertising and collecting status, are unsatisfactory in most countries and regions. Thus, some scholars proposed an alternative disposal practice that is to provide incentives to customers. This study aims to compare a Single Model (advertising only) with a Joint Model (advertising with take-back pricing) in a two-echelon reverse supply chain (RSC) that is composed of one disposer and one collector. In each model, four games (non-cooperative, collector as the Stackelberg leader, disposer as the Stackelberg leader, and cooperative) were established in order to identify the optimal pricing and advertising strategies for both members. The results of the study indicate that there is a Pareto dominant range for Joint Model compared to Single Model, whereas Single Model has no Pareto improvement in any games. Furthermore, in non-cooperative games of Joint Model, it is better to implement the leader-follower structure rather than simultaneous movement structure. Additionally, it is verified that the cooperative game is feasible, which leads to the cooperation between the disposer and the collector, and the extra profit from the cooperation can be shared based on the Nash bargaining game. However, in Single Model, it is better for the disposer to act as a channel leader and the collector figures the follower.