ML Anthology

When Does Schwartz Conjecture Hold?

Matthias Mnich, Yash Raj Shrestha, Yongjie Yang
IJCAI 2015 pp. 603-609
/ijcai/2015/mnich2015ijcai-schwartz/

Abstract

In 1990, Thomas Schwartz proposed the conjecture that every nonempty tournament has a unique minimal TEQ-retentive set (TEQ stands for tournament equilibrium set). A weak variant of Schwartz's Conjecture was recently proposed by Felix Brandt. However, both conjectures were disproved very recently by two counterexamples. In this paper, we prove sufficient conditions for infinite classes of tournaments that satisfy Schwartz's Conjecture and Brandt's Conjecture. Moreover, we prove that TEQ can be calculated in polynomial time in several infinite classes of tournaments. Furthermore, our results reveal some structures that are forbidden in every counterexample to Schwartz's Conjecture.

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Cite

Text

Mnich et al. "When Does Schwartz Conjecture Hold?." International Joint Conference on Artificial Intelligence, 2015.

Markdown

[Mnich et al. "When Does Schwartz Conjecture Hold?." International Joint Conference on Artificial Intelligence, 2015.](https://mlanthology.org/ijcai/2015/mnich2015ijcai-schwartz/)

BibTeX

@inproceedings{mnich2015ijcai-schwartz,
  title     = {{When Does Schwartz Conjecture Hold?}},
  author    = {Mnich, Matthias and Shrestha, Yash Raj and Yang, Yongjie},
  booktitle = {International Joint Conference on Artificial Intelligence},
  year      = {2015},
  pages     = {603-609},
  url       = {https://mlanthology.org/ijcai/2015/mnich2015ijcai-schwartz/}
}