Three-person Cooperative Game And Its Application In Decision Making Process Of Hierarchical Organizations

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

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