Coalition Formation Games and Social Ranking Solutions

Abstract

**Read paper on the following link:** https://ifaamas.org/Proceedings/aamas2022/pdfs/p862.pdf **Abstract:** A social ranking solution, or, briefly, a social ranking, over a set N is defined as a map assigning to each coalitional relation (i.e. a ranking over subsets of N) another ranking over the single elements in N. Differently, coalition formation situations, and, in particular, hedonic games, mainly focus on partitions of the set N into disjoint coalitions, which are in general referred to as coalition structures. A coalition structure may be stable according to various notions of stability and the objective is to understand under which conditions a coalition structure is stable. In this paper we merge the framework of coalition formation with the one of social rankings to keep into account the effect of hierarchies within coalitions on the stability of coalition structures. We consider alternative classes of coalition formation games where the preferences of the agents over coalitions are induced by a social ranking. More precisely, agents compare coalition structures keeping into account both the relative ranking of coalitions to which they belong (according to a coalitional relation) and their position in the social ranking within each coalition. Constructive characterizations of the set of core-stable coalition structures are provided for alternative classes of hedonic games, together with an impossibility theorem on the existence of core-stable coalitions structures for (nonhedonic) coalition formation situations.