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.
more »
« less
Favoring Eagerness for Remaining Items: Designing Efficient, Fair, and Strategyproof Mechanisms
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.
more » « less- Award ID(s):
- 2106983
- NSF-PAR ID:
- 10466783
- Publisher / Repository:
- JAIR
- Date Published:
- Journal Name:
- Journal of Artificial Intelligence Research
- Volume:
- 76
- ISSN:
- 1076-9757
- Page Range / eLocation ID:
- 287 to 339
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Fair division is the problem of allocating a set of items among a set of agents in a fair and efficient way. It arises naturally in a wide range of real-life settings. Competitive equilibrium (CE) is a central solution concept in economics to study markets, and due to its remarkable fairness and efficiency properties (e.g., envy-freeness, proportionality, core stability, Pareto optimality), it is also one of the most preferred mechanisms for fair division even though there is no money involved. The vast majority of work in fair division focuses on the case of disposable goods, which all agents like or can throw away at no cost. In this paper, we consider the case of mixed manna under linear utilities where some items are positive goods liked by all agents, some are bads (chores) that no one likes, and remaining some agents like and others dislike. The recent work of Bogomolnaia et al. [13] initiated the study of CE in mixed manna. They establish that a CE always exists and maintains all the nice properties found in the case of all goods. However, computing a CE of mixed manna is genuinely harder than in the case of all goods due to the nonconvex and disconnected nature of the CE set. Our main result is a polynomial-time algorithm for computing a CE of mixed manna when the number of agents or items is constant.more » « less
-
more » « less
We study markets with mixed manna, where m divisible goods and chores shall be divided among n agents to obtain a competitive equilibrium. Equilibrium allocations are known to satisfy many fairness and efficiency conditions. While a lot of recent work in fair division is restricted to linear utilities and chores, we focus on a substantial generalization to separable piecewise-linear and concave (SPLC) utilities and mixed manna. We first derive polynomial-time algorithms for markets with a constant number of items or a constant number of agents. Our main result is a polynomial-time algorithm for instances with a constant number of chores (as well as any number of goods and agents) under the condition that chores dominate the utility of the agents. Interestingly, this stands in contrast to the case when the goods dominate the agents utility in equilibrium, where the problem is known to be PPAD-hard even without chores.
-
more » « less
We study the problem of approximating maximum Nash social welfare (NSW) when allocating
m indivisible items amongn asymmetric agents with submodular valuations. TheNSW is a well-established notion of fairness and efficiency, defined as the weighted geometric mean of agents’ valuations. For special cases of the problem with symmetric agents and additive(-like) valuation functions, approximation algorithms have been designed using approaches customized for these specific settings, and they fail to extend to more general settings. Hence, no approximation algorithm with a factor independent ofm was known either for asymmetric agents with additive valuations or for symmetric agents beyond additive(-like) valuations before this work.In this article, we extend our understanding of the
NSW problem to far more general settings. Our main contribution is two approximation algorithms for asymmetric agents with additive and submodular valuations. Both algorithms are simple to understand and involve non-trivial modifications of a greedy repeated matchings approach. Allocations of high-valued items are done separately by un-matching certain items and re-matching them by different processes in both algorithms. We show that these approaches achieve approximation factors ofO (n ) andO (n logn ) for additive and submodular cases, independent of the number of items. For additive valuations, our algorithm outputs an allocation that also achieves the fairness property of envy-free up to one item (EF1 ).Furthermore, we show that the
NSW problem under submodular valuations is strictly harder than all currently known settings with an\(\frac{\mathrm{e}}{\mathrm{e}-1}\) \(\frac{\mathrm{e}}{\mathrm{e}-1}\) -
We revisit the well-studied problem of designing mechanisms for one-sided matching markets, where a set of n agents needs to be matched to a set of n heterogeneous items. Each agent i has a value vij for each item j, and these values are private information that the agents may misreport if doing so leads to a preferred outcome. Ensuring that the agents have no incentive to misreport requires a careful design of the matching mechanism, and mechanisms proposed in the literature mitigate this issue by eliciting only the ordinal preferences of the agents, i.e., their ranking of the items from most to least preferred. However, the efficiency guarantees of these mechanisms are based only on weak measures that are oblivious to the underlying values. In this paper we achieve stronger performance guarantees by introducing a mechanism that truthfully elicits the full cardinal preferences of the agents, i.e., all of the vij values. We evaluate the performance of this mechanism using the much more demanding Nash bargaining solution as a benchmark, and we prove that our mechanism significantly outperforms all ordinal mechanisms (even non-truthful ones). To prove our approximation bounds, we also study the population monotonicity of the Nash bargaining solution in the context of matching markets, providing both upper and lower bounds which are of independent interest.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1613/jair.1.13878
