A survey of approximability and inapproximability results for social welfare optimization in multiagent resource allocation

Multiagent resource allocation provides mechanisms to allocate bundles of resources to agents, where resources are assumed to be indivisible and nonshareable. A central goal is to maximize social welfare of such allocations, which can be measured in terms of the sum of utilities realized by the agen...

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Published in:	Annals of mathematics and artificial intelligence Vol. 68; no. 1-3; pp. 65 - 90
Main Authors:	Nguyen, Trung Thanh, Roos, Magnus, Rothe, Jörg
Format:	Journal Article
Language:	English
Published:	Dordrecht Springer Netherlands 01.07.2013 Springer Nature B.V
Subjects:	Agents (artificial intelligence) Artificial Intelligence Bundles Complex Systems Computer Science Focusing Mathematical models Mathematics Multiagent systems Optimization Reagents Resource allocation Utilities 68T99 Computational social choice Approximability 68Q17 Social welfare optimization Multiagent resource allocation
ISSN:	1012-2443, 1573-7470
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Abstract	Multiagent resource allocation provides mechanisms to allocate bundles of resources to agents, where resources are assumed to be indivisible and nonshareable. A central goal is to maximize social welfare of such allocations, which can be measured in terms of the sum of utilities realized by the agents ( utilitarian social welfare ), in terms of their minimum ( egalitarian social welfare ), and in terms of their product ( Nash product social welfare ). Unfortunately, social welfare optimization is a computationally intractable task in many settings. We survey recent approximability and inapproximability results on social welfare optimization in multiagent resource allocation, focusing on the two most central representation forms for utility functions of agents, the bundle form and the k-additive form . In addition, we provide some new (in)approximability results on maximizing egalitarian social welfare and social welfare with respect to the Nash product when restricted to certain special cases.
AbstractList	Multiagent resource allocation provides mechanisms to allocate bundles of resources to agents, where resources are assumed to be indivisible and nonshareable. A central goal is to maximize social welfare of such allocations, which can be measured in terms of the sum of utilities realized by the agents ( utilitarian social welfare ), in terms of their minimum ( egalitarian social welfare ), and in terms of their product ( Nash product social welfare ). Unfortunately, social welfare optimization is a computationally intractable task in many settings. We survey recent approximability and inapproximability results on social welfare optimization in multiagent resource allocation, focusing on the two most central representation forms for utility functions of agents, the bundle form and the k-additive form . In addition, we provide some new (in)approximability results on maximizing egalitarian social welfare and social welfare with respect to the Nash product when restricted to certain special cases. Multiagent resource allocation provides mechanisms to allocate bundles of resources to agents, where resources are assumed to be indivisible and nonshareable. A central goal is to maximize social welfare of such allocations, which can be measured in terms of the sum of utilities realized by the agents (utilitarian social welfare), in terms of their minimum (egalitarian social welfare), and in terms of their product (Nash product social welfare). Unfortunately, social welfare optimization is a computationally intractable task in many settings. We survey recent approximability and inapproximability results on social welfare optimization in multiagent resource allocation, focusing on the two most central representation forms for utility functions of agents, the bundle form and the k-additive form. In addition, we provide some new (in)approximability results on maximizing egalitarian social welfare and social welfare with respect to the Nash product when restricted to certain special cases.
Author	Roos, Magnus Rothe, Jörg Nguyen, Trung Thanh
Author_xml	– sequence: 1 givenname: Trung Thanh surname: Nguyen fullname: Nguyen, Trung Thanh organization: Institut für Informatik, Heinrich-Heine-Univ. Düsseldorf – sequence: 2 givenname: Magnus surname: Roos fullname: Roos, Magnus email: roos@cs.uni-duesseldorf.de organization: Institut für Informatik, Heinrich-Heine-Univ. Düsseldorf – sequence: 3 givenname: Jörg surname: Rothe fullname: Rothe, Jörg organization: Institut für Informatik, Heinrich-Heine-Univ. Düsseldorf
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