Hedonic Games with Graph-restricted Communication

We study hedonic coalition formation games in which cooperation among the players is restricted by a graph structure: a subset of players can form a coalition if and only if they are connected in the given graph. We investigate the complexity of finding stable outcomes in such games, for several notions of stability. In particular, we provide an efficient algorithm that finds an individually stable partition for an arbitrary hedonic game on an acyclic graph. We also introduce a new stability concept -in-neighbor stability- which is tailored for our setting. We show that the problem of finding an in-neighbor stable outcome admits a polynomial-time algorithm if the underlying graph is a path, but is NP-hard for arbitrary trees even for additively separable hedonic games; for symmetric additively separable games we obtain a PLS-hardness result

Boolean Hedonic Games

We study hedonic games with dichotomous preferences. Hedonic games are cooperative games in which players desire to form coalitions, but only care about the makeup of the coalitions of which they are members; they are indifferent about the makeup of other coalitions. The assumption of dichotomous preferences means that, additionally, each player's preference relation partitions the set of coalitions of which that player is a member into just two equivalence classes: satisfactory and unsatisfactory. A player is indifferent between satisfactory coalitions, and is indifferent between unsatisfactory coalitions, but strictly prefers any satisfactory coalition over any unsatisfactory coalition. We develop a succinct representation for such games, in which each player's preference relation is represented by a propositional formula. We show how solution concepts for hedonic games with dichotomous preferences are characterised by propositional formulas.Comment: This paper was orally presented at the Eleventh Conference on Logic and the Foundations of Game and Decision Theory (LOFT 2014) in Bergen, Norway, July 27-30, 201

Farsighted Stable Sets

A coalition is usually called stable if nobody has an immediate incentive to leave or to enter the coalition since he does not improve his payoff. This myopic behaviour does not consider further deviations which can take place after the first move. Chwe (1994) incorporated the idea of a farsighted behaviour in his definition of large consistent set (LCS). In some respects, we propose a different idea of dominance relation based on indirect dominance and on a different concept of belief on moving coalitions' behavior. A notion of stability for a coalitional game is introduced by taking into account the different degree of risk/safety of any player participating in a move. Some results about uncovered sets, internal stability are investigated. By exploiting our dominance and stability concepts, the prisoner's dilemma in coalitional form and its Nash equilibrium are studied. Some examples illustrating the differences between the largest consistent set, our stable set and stable set due to von Neumann and Morgenstern (1947) are presented.

Novel Hedonic Games and Stability Notions

We present here work on matching problems, namely hedonic games, also known as coalition formation games. We introduce two classes of hedonic games, Super Altruistic Hedonic Games (SAHGs) and Anchored Team Formation Games (ATFGs), and investigate the computational complexity of finding optimal partitions of agents into coalitions, or finding - or determining the existence of - stable coalition structures. We introduce a new stability notion for hedonic games and examine its relation to core and Nash stability for several classes of hedonic games