Besner, Manfred (2020): Values for level structures with polynomialtime algorithms, relevant coalition functions, and general considerations.
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Abstract
Exponential runtimes of algorithms for TUvalues like the Shapley value are one of the biggest obstacles in the practical application of otherwise axiomatically convincing solution concepts of cooperative game theory. We discuss how the hierarchical structure of a level structure improves the runtimes compared to an unstructured set of players. As examples, we examine the Shapley levels value, the nested Shapley levels value, and, as a new LSvalue, the nested Owen levels value. Polynomialtime algorithms for these values (under ordinary conditions) are provided. Furthermore, we introduce relevant coalition functions where all coalitions which are not relevant for the payoff calculation have a Harsanyi dividend of zero. By these coalition functions, our results shed new light on the computation of values of the Harsanyi set and many values from extensions of this set.
Item Type:  MPRA Paper 

Original Title:  Values for level structures with polynomialtime algorithms, relevant coalition functions, and general considerations 
Language:  English 
Keywords:  Cooperative game · Polynomialtime algorithm · Level structure · (Nested) Shapley/Owen (levels) value · Harsanyi dividends 
Subjects:  C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C71  Cooperative Games 
Item ID:  99355 
Depositing User:  Manfred Besner 
Date Deposited:  30 Mar 2020 11:18 
Last Modified:  30 Mar 2020 11:18 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/99355 
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