Collusion properties of coalition values for games in characteristic function form

This paper provides some new properties of coalition values which are blockability value and viability value. The investigated properties are related to coalition collusion within games in characteristic function form. Coalition proxy agreement and coalition association agreement of games in characteristic function form are defined. It turns out that the sum of blockability value of two coalitions which do not have common members and one coalition is a dummy coalition does not decrease if there exists a coalition proxy agreement between these two coalitions. It is also verified that the sum of blockability value of two coalitions which have no common members with coalition association agreement is equal to or less than the value with coalition proxy agreement in a convex game. Some propositions which show that the collusion properties of viability value are opposite to the collusion properties of blockability value are provided. A new axiom relevant to coalition collusion is proposed, and it is confirmed that blockability value satisfies the proposed axiom. A counterexample which shows that viability value does not always satisfy the proposed axiom is given.