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.
Communication complexity of discrete fair division
This paper initiates the study of the communication complexity of fair division with indivisible goods. It focuses on some of the most well-studied fairness notions (envy-freeness, proportionality, and approximations thereof) and valuation classes (submodular, subadditive and unrestricted). Within these
parameters, the results completely resolve whether the communication complexity of computing a fair allocation (or determining that none exist) is polynomial or exponential (in the number of goods), for every combination of fairness notion, valuation class, and number of players, for both deterministic and randomized protocols.
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- Award ID(s):
- 1813188
- PAR ID:
- 10096615
- Date Published:
- Journal Name:
- SODA '19 Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms
- Page Range / eLocation ID:
- 2014-2033
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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