Three-Person Cooperative Game and its Application in Decision Making Process of Hierarchical Organizations
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Date
2007-08
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Addis Ababa University
Abstract
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
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Keywords
Three-Person Cooperative, Game and its Application in Decision