A Direct Method of Interval Banzhaf Values of Interval Cooperative Games

Collaborative Resource Sharing Game Based Cloud-Edge Offload Computing Orchestration Scheme

“…The IBV is not only well-defined for every possible interval games, but also is median-indifferent on the class of size monotonic interval games. By using the interval subtraction operator, it can be explicitly obtained through using only the lower and upper bounds of the coalitions' interval payoffs [8]- [10].…”

“…The IBV satisfies the additivity, symmetry, anonymity, invariance, null player property, and dummy player property [10]. For example, let < 𝑁, 𝜈̅ > be a cooperative interval game with 𝑁 = {1, 2, 3} and 𝜈̅ (1) = 𝜈̅ (13) = [7,7] , 𝜈̅ (12) = [12,17] , 𝜈̅ (123) = [24, 29] and 𝜈̅ (𝑆) = [0,0] otherwise.…”

“…where 𝑝 𝑚 , 𝑝 𝑀 are the minimum and maximum price, respectively. According to (10), the price 𝑝 ℳ ℬ 𝑖 𝔓 is dynamically decided. Based on the 𝑝 ℳ ℬ 𝑖 𝔓 , the 𝜑 ℳ ℬ 𝑖 𝔓 is split into two parts 𝑥 ℳ ℬ 𝑖 and 𝑥 𝔓 , which are finally assigned to the ℳ ℬ 𝑖 and 𝔓, respectively.…”

“…Step 6: In the 𝔾 𝒞 game, each individual ℳ negotiates with the 𝔓, sequentially. To decide the offloading service price for each 〈ℳ ℬ 1≤𝑖≤𝑛 , 𝔓〉 pair, the price based utility functions of ℳ ℬ 𝑖 and 𝔓 are defined according to (9), and the 𝑝 ℳ ℬ 𝑖 𝔓 is decided according to (10).…”

“…A 𝑛-person interval cooperative game is expressed with an ordered-pair 〈𝑁, 𝜈̅ 〉, where 𝜈̅ is the interval characteristic function of players' coalitions and 𝜈̅ (∅) = [0,0] . Generally, for any coalition 𝑆 ⊆ 𝑁 , 𝜈̅ (𝑆) is denoted by the interval [𝜈 𝐿 (𝑆), 𝜈 𝑈 (𝑆)], where 𝜈 𝐿 (𝑆) ≤ 𝜈 𝑈 (𝑆)[9]-[10],[13].In the following,…”