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

Nguyen, Trung Thanh; Roos, Magnus; Rothe, Jörg

doi:10.1007/s10472-012-9328-4

Cited by 34 publications

(19 citation statements)

References 44 publications

(35 reference statements)

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“…The problem of computing an MNW allocation is known to be strongly N Phard [Nguyen et al 2013]. One of our main contributions is the algorithm we devised for computing an MNW allocation for the form of valuations elicited on Spliddit, in which a player is required to divide 1000 points among the available goods.…”

Section: Our Resultsmentioning

confidence: 99%

“…It is known that computing an exact MNW allocation is N P-hard even for 2 players with identical additive valuations, due to a simple reduction from the N P-hard problem PARTITION [Nguyen et al 2013;Ramezani and Endriss 2010]. Our goal in this section is to develop a fast implementation of the MNW solution, despite this obstacle.…”

Section: Methodsmentioning

confidence: 99%

“…This in turn ensures that the utilities to the players will also be integral, and not more than 1000. In theory, this does not help us: due to a known reduction from a strongly N P-complete problem -Exact Cover by 3-Sets (X3C) -to the problem of computing an MNW allocation [Nguyen et al 2013], we cannot hope for a pseudopolynomial-time algorithm (i.e., a polynomialtime algorithm for Spliddit-like valuations). In practice, however, this structure of the valuations can be leveraged to convert the non-linear objective into a linear objective:…”

Section: Methodsmentioning

confidence: 99%

See 2 more Smart Citations

The Unreasonable Fairness of Maximum Nash Welfare

Caragiannis

Kurokawa

Moulin

et al. 2016

Proceedings of the 2016 ACM Conference on Economics and Computation

179

167

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The maximum Nash welfare (MNW) solution -which selects an allocation that maximizes the product of utilities -is known to provide outstanding fairness guarantees when allocating divisible goods. And while it seems to lose its luster when applied to indivisible goods, we show that, in fact, the MNW solution is unexpectedly, strikingly fair even in that setting. In particular, we prove that it selects allocations that are envy free up to one good -a compelling notion that is quite elusive when coupled with economic efficiency. We also establish that the MNW solution provides a good approximation to another popular (yet possibly infeasible) fairness property, the maximin share guarantee, in theory and -even more so -in practice. While finding the MNW solution is computationally hard, we develop a nontrivial implementation, and demonstrate that it scales well on real data. These results lead us to believe that MNW is the ultimate solution for allocating indivisible goods, and underlie its deployment on a popular fair division website.

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Section: Our Resultsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

The Unreasonable Fairness of Maximum Nash Welfare

Caragiannis

Kurokawa

Moulin

et al. 2016

Proceedings of the 2016 ACM Conference on Economics and Computation

179

167

View full text Add to dashboard Cite

show abstract

“…The computational complexity of the Nash social welfare has been studied for various types of valuation functions [32,14] (see [26] for a survey of the known results). For the types of valuations that we consider here, i.e., for additive valuations, this problem was recently shown to be NPhard [34,25].…”

Section: Computational Complexitymentioning

confidence: 99%

Approximating the Nash Social Welfare with Indivisible Items

Cole,

Gkatzelis

2015

Proceedings of the Forty-Seventh Annual ACM Symposium on Theory of Computing

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We study the problem of allocating a set of indivisible items among agents with additive valuations, with the goal of maximizing the geometric mean of the agents' valuations, i.e., the Nash social welfare. This problem is known to be NPhard, and our main result is the first efficient constant-factor approximation algorithm for this objective. We first observe that the integrality gap of the natural fractional relaxation is exponential, so we propose a different fractional allocation which implies a tighter upper bound and, after appropriate rounding, yields a good integral allocation.An interesting contribution of this work is the fractional allocation that we use. The relaxation of our problem can be solved efficiently using the Eisenberg-Gale program, whose optimal solution can be interpreted as a market equilibrium with the dual variables playing the role of item prices. Using this market-based interpretation, we define an alternative equilibrium allocation where the amount of spending that can go into any given item is bounded, thus keeping the highly priced items under-allocated, and forcing the agents to spend on lower priced items. The resulting equilibrium prices reveal more information regarding how to assign items so as to obtain a good integral allocation.

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“…Thus, artificially applied search costs can be used as a mechanism to improve market efficiency, if applied appropriately. Hence, efficiency is considered both in the individual agent level, i.e., individual agent utility, and in terms of the sum of utilities realized by the agents (utilitarian social welfare), both commonly considered in multi-agent settings [43].…”

Section: Introductionmentioning

confidence: 99%

Exploration costs as a means for improving performance in multiagent systems

Sarne

Aumann

2014

Ann Math Artif Intell

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We consider settings were agents are faced with several possible opportunities and need to choose one. Each opportunity may offer a different utility to the agent, and determining this utility may consume resources. The underlying costly exploration problem is termed "economic search", though its essence is different from the traditional search notion in artificial intelligence (e.g. BFS, IDDFA, and A*), as there is no underlying combinatorial structure to the opportunities. We study the effects that search costs can have on individual and aggregate utility in distributed multi-agent economic-search settings. Traditionally, in such setting, search costs are regarded as a market inefficiency, and, as such, as something to be avoided or reduced to a minimum. We show, in contrast, that in many search settings, the introduction of search costs can actually improve the aggregate social welfare, or even the expected utility of each and every individual agent. We note that the proceeds from the search costs are assumed to be wasted, with no one directly benefiting from them. We demonstrate the benefits of search costs in both one-sided and two-sided search settings, using standard, classical models from economic-search theory. For the designers of multiagent systems, the results imply that deliberate (and potentially artificial) increase of search costs should be considered as possible means to improving the system's overall performance.

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

Cited by 34 publications

References 44 publications

The Unreasonable Fairness of Maximum Nash Welfare

The Unreasonable Fairness of Maximum Nash Welfare

Approximating the Nash Social Welfare with Indivisible Items

Exploration costs as a means for improving performance in multiagent systems

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