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

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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.

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Authors and Affiliations

  1. Institut für Informatik, Heinrich-Heine-Univ. Düsseldorf, 40225, Düsseldorf, Germany

    Trung Thanh Nguyen, Magnus Roos & Jörg Rothe

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  1. Trung Thanh Nguyen
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  2. Magnus Roos
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  3. Jörg Rothe
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Correspondence to Magnus Roos.

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This work was supported in part by DFG grant RO-1202/14-1 and a DAAD grant for a PPP project in the PROCOPE programme.

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Nguyen, T.T., Roos, M. & Rothe, J. A survey of approximability and inapproximability results for social welfare optimization in multiagent resource allocation. Ann Math Artif Intell 68, 65–90 (2013). https://doi.org/10.1007/s10472-012-9328-4

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