Tree solutions and standardness for cycle-free graph games

Abstract

The average tree solution for cycle-free graph games is uniquely determined by component efficiency and component fairness. Component fairness states that the average changes of payoffs for players in two separated components of a tree are equal when a link is broken. Thus a small part of players, particularly a player who is linked only to one of other players, may influence the game greatly. Replacing component fairness with total component fairness that counts changes of payoffs of players in total, we propose the total tree solution. This solution is characterized by component efficiency and component standardness.