Tangle and Ultrafilter: Game Theoretical Interpretation

This paper extends the concept of filter on X into ( X ,  f ), where X is a finite underlying set and f is a symmetric submodular function from 2 X to N. Then, we show a cryptomorphism between a free ultrafilter and co-tangle on ( X ,  f ). The paper also provides game-theoretical interpretations of...

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Bibliographic Details
Published in:Graphs and combinatorics 2020-03, Vol.36 (2), p.319-330
Main Authors: Fujita, Takaaki, Yamazaki, Koichi
Format: Article
Language:English
Subjects:
Combinatorics
Engineering Design
Game theory
Mathematics
Mathematics and Statistics
Original Paper
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Summary:This paper extends the concept of filter on X into ( X ,  f ), where X is a finite underlying set and f is a symmetric submodular function from 2 X to N. Then, we show a cryptomorphism between a free ultrafilter and co-tangle on ( X ,  f ). The paper also provides game-theoretical interpretations of a branch decomposition tree and a free ultrafilter on ( X ,  f ).
ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-019-02085-4