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In the assignment problem, the goal is to assign indivisible items to agents who have ordinal preferences, efficiently and fairly, in a strategyproof manner. In practice, first-choice maximality, i.e., assigning a maximal number of agents their top items, is often identified as an important efficiency criterion and measure of agents' satisfaction. In this paper, we propose a natural and intuitive efficiency property, favoring-eagerness-for-remaining-items (FERI), which requires that each item is allocated to an agent who ranks it highest among remaining items, thereby implying first-choice maximality. Using FERI as a heuristic, we design mechanisms that satisfy ex-post or ex-ante variants of FERI together with combinations of other desirable properties of efficiency (Pareto-efficiency), fairness (strong equal treatment of equals and sd-weak-envy-freeness), and strategyproofness (sd-weak-strategyproofness). We also explore the limits of FERI mechanisms in providing stronger efficiency, fairness, or strategyproofness guarantees through impossibility results.
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This content will become publicly available on April 11, 2026
Strategyproof Matching of Roommates and Rooms
We initiate the study of matching roommates and rooms wherein the preferences of agents over other agents and rooms are complementary and represented by Leontief utilities. In this setting, 2n agents must be paired up and assigned to n rooms. Each agent has cardinal valuations over the rooms as well as compatibility values over all other agents. Under Leontief preferences, an agent’s utility for a matching is the minimum of the two values. We focus on the tradeoff between maximizing utilitarian social welfare and strategyproofness. Our main result shows that—in a stark contrast to the additive case— under binary Leontief utilities, there exist strategyproof mechanisms that maximize the social welfare. We further devise a strategyproof mechanism that implements such a welfare maximizing algorithm and is parameterized by the number of agents. Along the way, we highlight several possibility and impossibility results, and give upper bounds and lower bounds for welfare with or without strategyproofness.
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- PAR ID:
- 10625324
- Publisher / Repository:
- Proceedings of the AAAI Conference on Artificial Intelligence, 39(13)
- Date Published:
- Journal Name:
- Proceedings of the AAAI Conference on Artificial Intelligence
- Volume:
- 39
- Issue:
- 13
- ISSN:
- 2159-5399
- Page Range / eLocation ID:
- 13926 to 13934
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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