The $$\chi $$ χ value and team games

On the Stability of Couples

“…First, we have to prove that the partitions mentioned are χ-stable. This result can be deduced directly from Corollary 4 in [8]. In the second step, we show no other possible partitions are χ-stable.…”

“…, C p . From Theorem 6 in [8], we know that χ i (N, v, P ) > χ j (N, v, P ) > 0, i ∈ W, j ∈ M. Adding or removing a player would reduce the χ-payoff of the remaining player. Also, substituting a player i ∈ W by a player j ∈ M does not raise the χ-payoffs of the players in at least one new component.…”

“…The Wiese value and the χ-value are the only values for CS games that interpret components as active groups and account for outside options of the players. In [8], the χ-value is used for a first analysis of team games. 2 1 In contrast, the Owen value [5] interprets components as bargaining unions.…”