Tournament solutions based on cooperative game theory

Aleksei Kondratev () and Vladimir V. Mazalov ()
Additional contact information
Vladimir V. Mazalov: Karelian Research Center of Russian Academy of Sciences

International Journal of Game Theory, 2020, vol. 49, issue 1, No 6, 119-145

Abstract: Abstract A tournament can be represented as a set of candidates and the results from pairwise comparisons of the candidates. In our setting, candidates may form coalitions. The candidates can choose to fix who wins the pairwise comparisons within their coalition. A coalition is winning if it can guarantee that a candidate from this coalition will win each pairwise comparison. This approach divides all coalitions into two groups and is, hence, a simple game. We show that each minimal winning coalition consists of a certain uncovered candidate and its dominators. We then apply solution concepts developed for simple games and consider the desirability relation and the power indices which preserve this relation. The tournament solution, defined as the maximal elements of the desirability relation, is a good way to select the strongest candidates. The Shapley–Shubik index, the Penrose–Banzhaf index, and the nucleolus are used to measure the power of the candidates. We also extend this approach to the case of weak tournaments.

Keywords: Tournament solution; Simple game; Shapley–Shubik index; Penrose–Banzhaf index; Desirability relation; Uncovered set; MSC 91A12; MSC 91B14 (search for similar items in EconPapers)
JEL-codes: C44 C71 D71 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s00182-019-00681-5 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jogath:v:49:y:2020:i:1:d:10.1007_s00182-019-00681-5

Ordering information: This journal article can be ordered from
http://www.springer. ... eory/journal/182/PS2

DOI: 10.1007/s00182-019-00681-5

Access Statistics for this article

International Journal of Game Theory is currently edited by Shmuel Zamir, Vijay Krishna and Bernhard von Stengel

More articles in International Journal of Game Theory from Springer, Game Theory Society
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().