STUDY ON DIFFERENT HEDONIC GAMES AND THEORIES OF STABILITY - Anupriya (International Journal of Multidisciplinary Research and Studies, 2020)
One of the results of this kind of game is a partition of the player set, also known as a coalition structure. This refers to a collection of coalitions, whose union is equal to the set of players, but which cannot be joined pairwise with one another. Marriage difficulties and roommate problems (Gale and Shapley (1962), Roth and Sotomayor (1990)) can both be viewed as special examples of hedonic coalition formation games. In these games, each agent solely considers who will be his or her partner. Problems can arise in both of these situations. In point of fact, hedonic games are only condensed versions of more general games involving the creation of coalitions. In these games, the manner in which a coalition's total payout is to be distributed among its members is predetermined and made transparent to all agents. Hedonic coalition formation games are a powerful tool to model agent behavior in a variety of circumstances. A classic example is the stable marriage problem which seeks to pair off men and women from two equally-sized groups. In the stable marriage problem, a pair is said to be stable if there is no man-woman pair who both want to leave their assigned partners to form a new pair.