2 research outputs found
Testing Stability Properties in Graphical Hedonic Games
In hedonic games, players form coalitions based on individual preferences
over the group of players they belong to. Several concepts to describe the
stability of coalition structures in a game have been proposed and analyzed.
However, prior research focuses on algorithms with time complexity that is at
least linear in the input size. In the light of very large games that arise
from, e.g., social networks and advertising, we initiate the study of sublinear
time property testing algorithms for existence and verification problems under
several notions of coalition stability in a model of hedonic games represented
by graphs with bounded degree. In graph property testing, one shall decide
whether a given input has a property (e.g., a game admits a stable coalition
structure) or is far from it, i.e., one has to modify at least an
-fraction of the input (e.g., the game's preferences) to make it have
the property. In particular, we consider verification of perfection, individual
rationality, Nash stability, (contractual) individual stability, and core
stability. Furthermore, we show that while there is always a Nash-stable
coalition (which also implies individually stable coalitions), the existence of
a perfect coalition can be tested. All our testers have one-sided error and
time complexity that is independent of the input size
Representing and Solving Hedonic Games with Ordinal Preferences and Thresholds
International audienceWe propose a new representation setting for hedonic games, where each agent partitions the set of other agents into friends, enemies, and neutral agents, with friends and enemies being ranked. Under the assumption that preferences are monotonic (respectively, antimonotonic) with respect to the addition of friends (respectively, enemies), we propose a bipolar extension of the Bossong-Schweigert extension principle, and use this principle to derive the (partial) preferences of agents over coalitions. Then, for a number of solution concepts, we characterize partitions that necessarily (respectively, possibly) satisfy them, and identify the computational complexity of the associated decision problems. Alternatively, we suggest cardinal comparability functions in order to extend to complete preference orders consistent with the generalized Bossong-Schweigert order