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On the structure of stable tournament solutions
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Brandt, Felix, Brill, Markus, Seedig, Hans Georg and Suksompong, Warut (2018) On the structure of stable tournament solutions. Economic Theory, 65 (2). pp. 483-507. doi:10.1007/s00199-016-1024-x ISSN 0938-2259.
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Official URL: http://dx.doi.org/10.1007/s00199-016-1024-x
Abstract
A fundamental property of choice functions is stability, which, loosely speaking, prescribes that choice sets are invariant under adding and removing unchosen alternatives. We provide several structural insights that improve our understanding of stable choice functions. In particular, (1) we show that every stable choice function is generated by a unique simple choice function, which never excludes more than one alternative, (2) we completely characterize which simple choice functions give rise to stable choice functions, and (3) we prove a strong relationship between stability and a new property of tournament solutions called local reversal symmetry. Based on these findings, we provide the first concrete tournament—consisting of 24 alternatives—in which the tournament equilibrium set fails to be stable. Furthermore, we prove that there is no more discriminating stable tournament solution than the bipartisan set and that the bipartisan set is the unique most discriminating tournament solution which satisfies standard properties proposed in the literature.
Item Type: | Journal Article | ||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science | ||||||||
Journal or Publication Title: | Economic Theory | ||||||||
Publisher: | Springer | ||||||||
ISSN: | 0938-2259 | ||||||||
Official Date: | March 2018 | ||||||||
Dates: |
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Volume: | 65 | ||||||||
Number: | 2 | ||||||||
Page Range: | pp. 483-507 | ||||||||
DOI: | 10.1007/s00199-016-1024-x | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access |
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