Sequential Resource Trading Using Comparison-Based Gradient Estimation

Autonomous agents interact with other agents of unknown preferences to share resources in their environment. We explore sequential trading for resource allocation in a setting where two greedily rational agents sequentially trade resources from a finite set of categories. Each agent has a utility function that depends on the amount of resources it possesses in each category. The offering agent makes trade offers to improve its utility without knowing the responding agent's utility function, and the responding agent only accepts offers that improve its utility. We present an algorithm for the offering agent to estimate the responding agent's gradient (preferences) and make offers based on previous acceptance or rejection responses. The algorithm's goal is to reach a Pareto-optimal resource allocation state while ensuring that the utilities of both agents improve after every accepted trade. We show that, after a finite number of consecutively rejected offers, the responding agent is at a near-optimal state, or the agents' gradients are closely aligned. We compare the proposed algorithm against various baselines in continuous and discrete trading scenarios and show that it improves the societal benefit with fewer offers.