Approximately Socially-Optimal Decentralized Coalition Formation

Abstract

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 costsharing 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 realworld P2P energy sharing project.

Geographical Peer Matching for P2P Energy Sharing

“…Such an exchange can get instantly gratified leading to a local trading market [30,38]. Since there is an inherent infrastructure cost to allow and maintain energy exchanges between a large number of end-users, exchanges have been restrained to occur within independent longterm communities of end-users [22,18,4,11] that can last for month(s) or year(s). At the end of predetermined billing periods, each user pays an electricity bill taking into account all exchanges that occurred within the said period.…”

“…10min) are formed to cover a single timeslot where game-theoretic approaches are used to optimize the individual gains among other things [33]. On the contrary, long-term coalitions [22,18,4,11] seek to form communities that will take coordinated decisions within the same group of peers over months to years. Often also associated with geographical closeness, the long-term communities present many advantages from an infrastructure point of view, being able to better regulate local loadbalancing of distributed energy resources, providing higher local self-sufficiency and/or reducing the local peak demand.…”

“…Often also associated with geographical closeness, the long-term communities present many advantages from an infrastructure point of view, being able to better regulate local loadbalancing of distributed energy resources, providing higher local self-sufficiency and/or reducing the local peak demand. Research on optimizing the gain outcome from the peering process using constrained optimization has focused on different aspects: how communications are handled [22], reaching stable partitions [5,4], finding optimal resources based on community sizes [18], privacy aspects and amount of data transmitted over the network [20,10,11], etc. Small neighborhoods have been shown to provide a high share of possible gain while being favorable in terms of data exchange [11] and different matching were previously studied in [5,4], based upon stable partitions (i.e., nodes with self-interest) and on a cost-sharing mechanism known beforehand.…”

“…Chau et al [5] have investigated stable partitioning, i.e., a given partitioning can be rejected if any group of peers would gain more by forming a different one, similar to the stable marriage [25] problem for pairs. Zhou et al [39,4] expand the partitioning to communities of size k > 2 and evaluate partition-forming algorithms for groups of size 2 or 3 over a set of 30 households. Duvignau et al [10,11] advocate small-scale communities made of a few peers only (2 to 5) claiming that smaller groups are both efficient in terms of data and cost.…”

“…Motivations Current state-of-the-art [18,4,11] relies on exhaustive search to compute the optimal solution from datasets containing only a small number of nodes. To scale up towards large systems, we introduce the Geographical Peer Matching (GPM) problem that consists in forming the energy communities based on both geographical information about the peers as well as their local matching preferences.…”