Coalition-hierarchical game under uncertainty conditions

An optimization problem in a coalition-hierarchical game under uncertainty conditions is formulated. In the game, information assumptions are that the player of the high hierarchical level (controlling Center) and each low-level coalition estimates uncertainty in its own way. The Center constructs its strategy from the maximum condition for its own payoff function and its minimum in uncertainty. The relationships between coalitions are built upon the guaranteeing absolute active equilibrium understood in the sense of providing the players with guaranteed payoff under the actual uncertainty. The guaranteed uncertainty is obtained with the help of Slater principle. The total equilibrium in the game is called CH-equilibrium. For a quadratic game version, sufficient optimality conditions are obtained. A numerical procedure for solving the game is described and an example is given.