Core Non-emptiness Checking in Hedonic Games via Difference Logic

Abstract

Hedonic games provide a useful formalism to model cooperation of self-interested agents. This is due to the fact that all stable partitionings of a set of agents into disjoint coalitions can be represented as a core of a hedonic game. An important problem in this setting is to decide whether or not a given hedonic game allows for a stable partitioning of the players into disjoint coalitions. This amounts to checking whether a core of a hedonic game is non-empty which is known to be an NP-complete problem. In this paper, a novel method to check the core non-emptiness in hedonic games is presented. A compact characterisation of hedonic game core non-emptiness is given in difference logic. This characterisation leads to employment of difference logic satisfiability testing algorithms to check core non-emptiness in hedonic games. An implementation of the method is reported together with experimental results to demonstrate the usefulness and applicability of the presented approach.