Approximately Socially-Optimal Decentralized Coalition Formation
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Coalition formation is a central part of social interactions. In the emerging era of social peer-to-peer interactions (e.g., sharing economy), coalition formation will be often carried out in a decentralized manner, based on participants' individual preferences. A likely outcome will be a stable coalition structure, where no group of participants could cooperatively opt out to form another coalition that induces higher preferences to all its members. Remarkably, there exists a number of fair cost-sharing mechanisms (e.g., equal-split, proportional-split, egalitarian and Nash bargaining solutions of bargaining games) that model practical cost-sharing applications with desirable properties of stable coalition structure, such as its existence and a small strong price-of-anarchy (SPoA) for approximating the social optimum. In this paper, we close several gaps on the results of decentralized coalition formation: (1) We establish a logarithmic lower bound on SPoA, and hence, show several previously known fair cost-sharing mechanisms are the best practical mechanisms with minimal SPoA. (2) We improve the SPoA of egalitarian and Nash bargaining cost-sharing mechanisms to match the lower bound. (3) We derive the SPoA of a mix of different cost-sharing mechanisms. (4) We present a decentralized algorithm to form a stable coalition structure. (5) Finally, we apply our results to a novel application of peer-to-peer energy sharing that allows households to jointly utilize mutual energy resources. We present an empirical study of decentralized coalition formation in a real-world P2P energy sharing project.
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