  In this paper the Shapley value of digraph (directed graph) games are
considered. Digraph games are transferable utility (TU) games with limited
cooperation among players, where players are represented by nodes. A
restrictive relation between two adjacent players is established by a directed
line segment. Directed path, connecting the initial player with the terminal
player, form the coalition among players. A dominance relation is established
between players and this relation determines whether or not a player wants to
cooperate. To cooperate, we assume that a player joins a coalition where he/she
is not dominated by any other players.The Shapley value is defined as the
average of marginal contribution vectors corresponding to all permutations that
do not violate the subordination of players. The Shapley value for cyclic
digraph games is calculated and analyzed. For a given family of characteristic
functions, a quick way to calculate Shapley values is formulated.
