Three-Person Cooperative Game and its Application in Decision Making Process of Hierarchical Organizations

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Addis Ababa University


The solution of an n-level linear problem, when the levels make decisions se- quentially and independently, is not necessarily pareto-optimal, i.e.there exist feasible points which o®er increased payo®s to some levels without diminish- ing the payo®s to other levels. These increased payo®s may be obtained if the levels coalesce. In particular if the number of decision makers on each level form coalition to work cooperatively they can get a better payo®. A game theoretic methodol- ogy for predicting coalition formation in the decision makers on each level is presented. The problem is modeled as an abstract game. If a core exists for the characteristic function game, then there exists a set of enforceable points which o®er the increased payo®s available to the system, but a core may not exist. When the core exist, for games with non-empty cores, it would be an advantageous property for a power index to assign values to the players that comprise a solution in the core. We use Shapley value, as a solution concept, which has got a drawback that it might not always been an element of the core. So we take the Willick's power index as a best solution concept, which has got a better relation with the core than Shapley. The n-level Stackleberg problem, which represent a class of n-level linear problem, as a special case the 3-level Stackleberg problem, is de¯ned. In the university budget allocation system coalition among decision makers in each level, science faculty, is used to demonstrate the suggested methodology



Three-Person Cooperative, Game and its Application in Decision