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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 piecewiselinear and concave (SPLC) utilities and mixed manna. We first derive polynomialtime algorithms for markets with a constant number of items or a constant number of agents. Our main result is a polynomialtime 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 PPADhard even without chores.
more » « less Award ID(s):
 1942321
 NSFPAR ID:
 10491726
 Publisher / Repository:
 Journal of Artificial Intelligence Research
 Date Published:
 Journal Name:
 Journal of Artificial Intelligence Research
 Volume:
 78
 ISSN:
 10769757
 Page Range / eLocation ID:
 1201 to 1219
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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