A generalized optimization model for cooperative games / Marwa Mostafa Sabry Mostafa ; Supervised Ihab Ahmed Fahmy Elkhodary , Assem Abdelfattah Tharwat

Thesis (Ph.D.) - Cairo University - Faculty of Computers and Artificial Intelligence - Department of Operations Research and Decision Support

Cooperative games is a branch of game theory in which players cooperate together forming coalitions to get more benefits. Realistic cooperative situations are exposed to uncertain worth or payoff of the coalitions, and according to the type of such uncertainty for coalition value, the cooperative games are either fuzzy or stochastic cooperative ones. In fuzzy games, coalition utilities are expressed using fuzzy numbers, while in stochastic games, the utilities are random variables with known probability density functions. The problem addressed by fuzzy and stochastic cooperative games is that of distributing the worth of the coalitions among their members in a reasonable way. For fuzzy cooperative games, the main solution concept is the Shapley value and its extension of the Hukuhara-Shapley function in which the explicit form of Shapley function is based on the Hukuhara difference and the Choquet Integral. However, it has a major limitation since it requires the existence of Hukuhara condition between fuzzy numbers, which does not always exist. In addition, computation of the Hukuhara-Shapley value requires an excessive number of calculations, particularly; it requires finding the crisp Shapley values prior to solving for fuzzy coalitions, which increases the complexity of solution. For stochastic cooperative games, many researchers came with several equivalent formulations of the Shapley value for cooperative games. But each formulation has its limitation when solving the game in the type of randomness of the characteristic function value. Moreover, previous approaches considered the imputation of the game in a stochastic setting as fixed proportions not allowing utilities to be expressed as random variables

Issued also as CD