On Shortest Path Interval Games

In this paper, a kind of shortest path interval game is studied. The following two theorems are obtained. (1) When the coalition S owns the path, and the condition W(S)=[W_l(S),W_l(S)+c] is true for some fixed c≥0, then there exists no-empty interval core; (2) When the coalition S owns the path, and the condition W(S)=[W_l(S), (1+θ)W_l(S)] is true for some fixed θ≥0, then there exists no-empty interval core. By using the concept of the point core of the game introduced by S. Zeynep Alparslan Gök, the lower point game and upper point game are defined. Using the concept of compositive defined in this paper, the interval game is translated to two point games. By introducing the concept of critical value, it bound the range of incomes of the game. Finally, the distribution of the interval core simplified by defining the minimal supporting set.