The regulation of platforms has been a hot topic, particularly in Europe with the Digital Markets Act (DMA) passed in 2022. The purpose of this paper is to design a mathematical model representing a game between long-term revenue-oriented platforms in competition playing with their ranking strategy of items. The objective of platforms is to apply a trade-off between short-term revenue from each visit by displaying most profitable items and long-term number of visits due to the satisfaction of users from the relevance of the displayed items. We analyze the output of the game and the impact of proposed regulation rules on platforms and users.