  We study the problem of decision-making in the setting of a scarcity of
shared resources when the preferences of agents are unknown a priori and must
be learned from data. Taking the two-sided matching market as a running
example, we focus on the decentralized setting, where agents do not share their
learned preferences with a central authority. Our approach is based on the
representation of preferences in a reproducing kernel Hilbert space, and a
learning algorithm for preferences that accounts for uncertainty due to the
competition among the agents in the market. Under regularity conditions, we
show that our estimator of preferences converges at a minimax optimal rate.
Given this result, we derive optimal strategies that maximize agents' expected
payoffs and we calibrate the uncertain state by taking opportunity costs into
account. We also derive an incentive-compatibility property and show that the
outcome from the learned strategies has a stability property. Finally, we prove
a fairness property that asserts that there exists no justified envy according
to the learned strategies.
