CHARACTERIZATION OF SOLUTIONS FOR BICOOPERATIVE GAMES BY USING REPRESENTATION THEORY

When analyzing solutions for bicooperative games as well as classical cooperative games, traditional approaches regard both of games and payoff vectors as linear spaces, but in this paper, we present another approach to analyze solutions from the viewpoint of representation of the symmetric group. First, we regard the space of games as a representation of the symmetric group. Then, by using tools of representation theory, we obtain a decomposition of the space and specify useful subrepresentations. Exploiting this decomposition, we show an explicit formula of linear symmetric solutions. Additionally, we also show expressions of linear symmetric solutions restricted by parts of the axioms of the Shapley value for bicooperative games.