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We consider a trading marketplace that is populated by traders with diverse trading strategies and objectives. The marketplace allows the suppliers to list their goods and facilitates matching between buyers and sellers. In return, such a marketplace typically charges fees for facilitating trade. The goal of this work is to design a dynamic fee schedule for the marketplace that is equitable and profitable to all traders while being profitable to the marketplace at the same time (from charging fees). Since the traders adapt their strategies to the fee schedule, we present a reinforcement learning framework for simultaneously learning a marketplace fee schedule and trading strategies that adapt to this fee schedule using a weighted optimization objective of profits and equitability. We illustrate the use of the proposed approach in detail on a simulated stock exchange with different types of investors, specifically market makers and consumer investors. As we vary the equitability weights across different investor classes, we see that the learnt exchange fee schedule starts favoring the class of investors with the highest weight. We further discuss the observed insights from the simulated stock exchange in light of the general framework of equitable marketplace mechanism design.