Multiagent resource allocation deals with distributing (bundles) of resources to agents that specify utility functions over bundles. A natural and important problem in this field is social welfare optimization. We assume resources to be indivisible and nonshareable and that utility functions are represented by the k-additive form or as straight-line programs. We prove NP-completeness for egalitarian and Nash product social welfare optimization for straight-line program representation of utility functions. In addition, we show that social welfare optimization by the Nash product in the 1-additive form is hard to approximate, yet we also give fully polynomial-time approximation schemes for egalitarian and Nash product social welfare optimization in the 1-additive form with a fixed number of agents.
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