Practical Application of Cooperative Solution Concepts for Distribution Problems: An Analysis of Selected Game Theoretic Solution Concepts from an Economic Point of View (pp. 19-38)

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Authors: Susanne Jene and Stephan Zelewski

Abstract: Most scientific publications on the subject of cooperative solution concepts only
analyze these concepts from a game theoretic point of view. Therefore, it is often
disregarded whether the cooperative solution concepts can be put into economic practice.
One example for a possible application of cooperative solution concepts in practice is the
fair distribution of collectively earned profits in cooperations of legally independent
corporations. This chapter intends to analyze whether cooperative solution concepts are
able to solve this practical problem.
In the first part of this chapter two cooperative solution concepts are compared from
a game theoretic point of view. The first cooperative solution concept is the widely
known Shapley value that can be described as a rather “classic” cooperative solution
concept. The second one is a younger, more innovative solution concept called χ-value.
These two cooperative solution concepts are compared with regard to the conditions and
assumptions they are based on and the characteristics of their resulting solutions, e.g. the
stability of a solution.
In the second part the two cooperative solution concepts are analyzed from an
economic point of view. For this purpose, criteria for a successful use of game theoretic
solution concepts applied on distribution problems in economic practice are introduced,
e.g. information requirements. Special attention is put on the fairness aspect, as a solution
concept can only be successfully used in practice if all business partners accept the
solution as fair. Lastly, a practical example is used to illustrate the specific numerical
application of the two solution concepts.
The findings of this chapter are of threefold kind. First, the variety of solution
concepts and their results is illustrated by the comparison of the Shapley value and the χ-
value. Secondly, with the help of the calculation example it is revealed which information
requirements and which other criteria have to be fulfilled in order to use the presented
solution concepts in practice. Thirdly, it is analyzed whether at least one of the solution
concepts is more likely to be put successfully into practice than the other.

Practical Application of Cooperative Solution Concepts for Distribution Problems: An Analysis of Selected Game Theoretic Solution Concepts from an Economic Point of View (pp. 19-38)