Cooperative game theory is a branch of (micro-)economics that studies the behavior of self-interested agents in strategic settings where binding agreements among agents are possible. Our aim in this book is to present a survey of work on the computational aspects of cooperative game theory. We begin by formally defining transferable utility games in characteristic function form, and introducing key solution concepts such as the core and the Shapley value. We then discuss two major issues that arise when considering such games from a computational perspective: identifying compact representations for games, and the closely related problem of efficiently computing solution concepts for games. We survey several formalisms for cooperative games that have been proposed in the literature, including, for example, cooperative games defined on networks, as well as general compact representation schemes such as MC-nets and skill games. As a detailed case study, we consider weighted voting games: a widely-us...

In the usual models of cooperative game theory, the outcome of a coalition formation process is either the grand coalition or a coalition structure that consists of disjoint coalitions. However, in many domains where coalitions are associated with tasks, an agent may be involved in executing more than one task, and thus may distribute his resources among several coalitions. To tackle such scenarios, we introduce a model for cooperative games with overlapping coalitions—or overlapping coalition formation (OCF) games. We then explore the issue of stability in this setting. In particular, we introduce a notion of the core, which generalizes the corresponding notion in the traditional (non-overlapping) scenario. Then, under some quite general conditions, we characterize the elements of the core, and show that any element of the core maximizes the social welfare. We also introduce a concept of balancedness for overlapping coalitional games, and use it to characterize coalition structures that can be extended to elements of the core. Finally, we generalize the notion of convexity to our setting, and show that under some natural assumptions convex games have a non-empty core. Moreover, we introduce two alternative notions of stability in OCF that allow a wider range of deviations, and explore the relationships among the corresponding definitions of the core, as well as the classic (non-overlapping) core and the Aubin core. We illustrate the general properties of the three cores, and also study them from a computational perspective, thus obtaining additional insights into their fundamental structure.

Cooperative game theory studies situations in which agents can benefit by working together. This article outlines the key concepts of cooperative game theory, and discusess the challenges that arise in applying these in AI applications.

Virtual Power Plants (VPPs) are fast emerging as a viable means of integrating small and distributed energy resources (DERs), like wind and solar, into the electricity supply network (Grid). VPPs are formed via the aggregation of a large number of DERs, so that they exhibit the characteristics of a traditional generator in terms of predictability and robustness. In this work, we promote the formation of such “cooperative” VPPs (CVPPs) using techniques from the field of distributed Artificial Intelligence and game theory. In particular, we design a payment mechanism that encourages DERs to join CVPPs with increased size and visibility to the network operator. Our method is based on strictly proper scoring rules and incentivises the provision of accurate predictions of expected electricity generation from member DERs, which aids in the planning of the supply schedule at the Grid. We empirically evaluate our approach using the real-world setting of 16 commercial wind farms in the UK, and we show that it incentivises real DERs to form CVPPs, and outperforms the current state of the art payment mechanism developed for this problem