The Distortion of Threshold Approval Matching
CoRR(2024)
摘要
We study matching settings in which a set of agents have private utilities
over a set of items. Each agent reports a partition of the items into approval
sets of different threshold utility levels. Given this limited information on
input, the goal is to compute an assignment of the items to the agents (subject
to cardinality constraints depending on the application) that (approximately)
maximizes the social welfare (the total utility of the agents for their
assigned items). We first consider the well-known, simple one-sided matching
problem in which each of n agents is to be assigned exactly one of n items.
We show that with t threshold utility levels, the distortion of deterministic
matching algorithms is Θ(√(n)) while that of randomized
algorithms is Θ(√(n)). We then show that our distortion bounds
extend to a more general setting in which there are multiple copies of the
items, each agent can be assigned a number of items (even copies of the same
one) up to a capacity, and the utility of an agent for an item depends on the
number of its copies that the agent is given.
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