IN-DEPTH ANALYSES OF THE REWARD STRUCTURES OF N- PERSON COOPERATIVE GAMES WITH SPECIFIED WINNING COALITIONS INVOLVING AT LEAST ONE MAJOR PLAYER (Published)
Explicit computational rewards were obtained for n- person cooperative games involving specific classes of players of different ranks by the construction and deployment of cardinality-based listing structure of combined sets of winning coalitions. The results were rigorously analyzed and validated with clearly derived mathematical relationships.
VOTING POWERS AND A FUNCTIONAL REPRESENTATION OF THE VOTING CLOUT OF UNITED NATIONS SECURITY COUNCIL MEMBERS WITH VETO POWER RELAXATION (Published)
An independent mathematical structure was developed for the computation of the voting powers of United Nations Security Council members using the Shapley value concept, cooperative games and deft constructions of coalition sets. The results, obtained through Microsoft Excel implementations show that each permanent member has more than ten times as much voting clout as all ten nonpermanent members put together. A sensitivity analysis-based theorem was formulated to address this unacceptable unwholesome lopsidedness in voting powers while preserving the veto status of permanent members.Finally the paper exploited the Shapley value concept to obtain mathematical formulations and representations of voting powers of the members subject to any resolution passing threshold of votes supported by at least a partial coalition of Permanent representatives. The solution expressions can be used to obtain various levels of voting powers by appropriate adjustments of the parameters, thus giving prescriptions for more equitable distribution of voting powers.