A Further Step Towards an Understanding of the Tournament Equilibrium Set
Yongjie Yang

TL;DR
This paper advances understanding of the tournament equilibrium set (TEQ) by classifying TEQ-retentive tournaments of small sizes, confirming Schwartz's Conjecture up to size 14, and exploring properties of TEQ-retentive sets.
Contribution
It provides a detailed classification of TEQ-retentive tournaments for sizes 4 to 7 and verifies Schwartz's Conjecture for tournaments up to size 14.
Findings
No TEQ-retentive tournaments of size 4.
Only 2 non-isomorphic TEQ-retentive tournaments of size 5.
26 non-isomorphic TEQ-retentive tournaments of size 7.
Abstract
We study some problems pertaining to the tournament equilibrium set (TEQ for short). A tournament is a TEQ-retentive tournament if there is a tournament which has a minimal TEQ-retentive set such that is isomorphic to . We study TEQ-retentive tournaments and achieve many significant results. In particular, we prove that there are no TEQ-retentive tournaments of size 4, only 2 non-isomorphic TEQ-retentive tournaments of sizes 5 and 6, respectively, and 26 non-isomorphic TEQ-retentive tournaments of size 7. For three tournaments and , we say is a -TEQ-retentive tournament if has two minimal TEQ-retentive sets and such that and are isomorphic to and , respectively. We show that there are no -retentive tournaments for and being small tournaments. Our results imply that…
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Taxonomy
TopicsGame Theory and Voting Systems · Advanced Graph Theory Research · Economic theories and models
