For the assignment problem where multiple indivis- ible items are allocated to a group of agents given their ordinal preferences, we design randomized mechanisms that satisfy first-choice maximality (FCM), i.e., maximizing the number of agents as- signed their first choices, together with Pareto- efficiency (PE). Our mechanisms also provide guarantees of ex-ante and ex-post fairness. The generalizedeager Boston mechanism is ex-ante envy-free, and ex-post envy-free up to one item (EF1). The generalized probabilistic Boston mech- anism is also ex-post EF1, and satisfies ex-ante ef- ficiency instead of fairness. We also show that no strategyproof mechanism satisfies ex-post PE, EF1, and FCM simultaneously. In doing so, we expand the frontiers of simultaneously providing efficiency and both ex-ante and ex-post fairness guarantees for the assignment problem.
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This content will become publicly available on March 25, 2025
Strategyproof Mechanisms for Group-Fair Obnoxious Facility Location Problems
We study the group-fair obnoxious facility location problems from the mechanism design perspective where agents belong to different groups and have private location preferences on the undesirable locations of the facility. Our main goal is to design strategyproof mechanisms that elicit the true location preferences from the agents and determine a facility location that approximately optimizes several group-fair objectives. We first consider the maximum total and average group cost (group-fair) objectives. For these objectives, we propose deterministic mechanisms that achieve 3-approximation ratios and provide matching lower bounds. We then provide the characterization of 2-candidate strategyproof randomized mechanisms. Leveraging the characterization, we design randomized mechanisms with improved approximation ratios of 2 for both objectives. We also provide randomized lower bounds of 5/4 for both objectives. Moreover, we investigate intergroup and intragroup fairness (IIF) objectives, addressing fairness between groups and within each group. We present a mechanism that achieves a 4-approximation for the IIF objectives and provide tight lower bounds.
more » « less- Award ID(s):
- 2302999
- PAR ID:
- 10538444
- Publisher / Repository:
- AAAI Conference on Artificial Intelligence
- Date Published:
- Journal Name:
- Proceedings of the AAAI Conference on Artificial Intelligence
- Volume:
- 38
- Issue:
- 9
- ISSN:
- 2159-5399
- Page Range / eLocation ID:
- 9832 to 9839
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Funding: The work of E. Balkanski was supported in part by the National Science Foundation [Grants CCF-2210501 and IIS-2147361]. The work of V. Gkatzelis and X. Tan was supported in part by the National Science Foundation [Grant CCF-2210502] and [CAREER Award CCF-2047907].
