Guaranteeing Maximin Shares: Some Agents Left Behind
| Autor: | Andrew Searns, Hadi Hosseini |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
FOS: Computer and information sciences
education.field_of_study ComputerSystemsOrganization_COMPUTERSYSTEMIMPLEMENTATION Computer Science - Artificial Intelligence Computation Population Approximation algorithm Minimax Combinatorics FOS: Economics and business Artificial Intelligence (cs.AI) Computer Science - Computer Science and Game Theory Key (cryptography) Economics - Theoretical Economics Theoretical Economics (econ.TH) Fraction (mathematics) Constant (mathematics) education Time complexity Mathematics Computer Science and Game Theory (cs.GT) |
| Zdroj: | IJCAI |
| DOI: | 10.48550/arxiv.2105.09383 |
| Popis: | The maximin share (MMS) guarantee is a desirable fairness notion for allocating indivisible goods. While MMS allocations do not always exist, several approximation techniques have been developed to ensure that all agents receive a fraction of their maximin share. We focus on an alternative approximation notion, based on the population of agents, that seeks to guarantee MMS for a fraction of agents. We show that no optimal approximation algorithm can satisfy more than a constant number of agents, and discuss the existence and computation of MMS for all but one agent and its relation to approximate MMS guarantees. We then prove the existence of allocations that guarantee MMS for $\frac{2}{3}$ of agents, and devise a polynomial time algorithm that achieves this bound for up to nine agents. A key implication of our result is the existence of allocations that guarantee $\text{MMS}^{\lceil{3n/2}\rceil}$, i.e., the value that agents receive by partitioning the goods into $\lceil{\frac{3}{2}n}\rceil$ bundles, improving the best known guarantee of $\text{MMS}^{2n-2}$. Finally, we provide empirical experiments using synthetic data. Comment: Full version of a paper accepted to IJCAI 2021 |
| Databáze: | OpenAIRE |
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