We consider a peer-to-peer logistics system, where the agents and the platform communicate in both directions in a multi-period setting. The goal of the platform is to select a subset of the requests to offer to each agent that would result in a maximum valued matching for the platform. The platform utilizes the agent's choice to learn about her preferences and improve the estimated decision mechanism of the agent. Through systematic experimentation, we first establish that at the earlier iterations and while the decision mechanism of the agent is not yet accurately estimated, a larger menu size could benefit the platform's overall gain better. However, after the estimates become more accurate through the learning process, a smaller menu size can further increase the overall benefits.
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