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Computing stable coalitions: approximation algorithms for reward sharing. (English) Zbl 1406.91122
Markakis, Evangelos (ed.) et al., Web and internet economics. 11th international conference, WINE 2015, Amsterdam, The Netherlands, December 9–12, 2015. Proceedings. Berlin: Springer (ISBN 978-3-662-48994-9/pbk; 978-3-662-48995-6/ebook). Lecture Notes in Computer Science 9470, 31-45 (2015).
Summary: Consider a setting where selfish agents are to be assigned to coalitions or projects from a set $$\mathcal {P}$$. Each project $$k\in \mathcal {P}$$ is characterized by a valuation function; $$v_k(S)$$ is the value generated by a set $$S$$ of agents working on project $$k$$. We study the following classic problem in this setting: “how should the agents divide the value that they collectively create?”. One traditional approach in cooperative game theory is to study core stability with the implicit assumption that there are infinite copies of one project, and agents can partition themselves into any number of coalitions. In contrast, we consider a model with a finite number of non-identical projects; this makes computing both high-welfare solutions and core payments highly non-trivial.
The main contribution of this paper is a black-box mechanism that reduces the problem of computing a near-optimal core stable solution to the well-studied algorithmic problem of welfare maximization; we apply this to compute an approximately core stable solution that extracts one-fourth of the optimal social welfare for the class of subadditive valuations. We also show much stronger results for several popular sub-classes: anonymous, fractionally subadditive, and submodular valuations, as well as provide new approximation algorithms for welfare maximization with anonymous functions. Finally, we establish a connection between our setting and simultaneous auctions with item bidding; we adapt our results to compute approximate pure Nash equilibria for these auctions.
For the entire collection see [Zbl 1326.68026].
##### MSC:
 91B15 Welfare economics 91A12 Cooperative games 68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.)
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##### References:
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