Similarity Suppresses Cyclicity: Why Similar Competitors Form Hierarchies
Christopher Cebra, and Alexander Strang

TL;DR
This paper explains why most real-world competitive systems tend to form hierarchies rather than cycles, showing that similarity and smooth performance functions promote transitivity, supported by theoretical proofs and evolution experiments.
Contribution
The paper introduces a general mechanism demonstrating how similarity and smoothness in performance functions promote transitivity in competitive systems, explaining the prevalence of hierarchies.
Findings
Similar competitors tend to compete transitively.
Evolutionary training promotes trait convergence and transitivity.
The mechanism is robust across various game types and performance functions.
Abstract
Competitive systems can exhibit both hierarchical (transitive) and cyclic (intransitive) structures. Despite theoretical interest in cyclic competition, which offers richer dynamics, and occupies a larger subset of the space of possible competitive systems, most real-world systems are predominantly transitive. Why? Here, we introduce a generic mechanism which promotes transitivity, even when there is ample room for cyclicity. Consider a competitive system where outcomes are mediated by competitor attributes via a performance function. We demonstrate that, if competitive outcomes depend smoothly on competitor attributes, then similar competitors compete transitively. We quantify the rate of convergence to transitivity given the similarity of the competitors and the smoothness of the performance function. Thus, we prove the adage regarding apples and oranges. Similar objects admit well…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsEvolutionary Game Theory and Cooperation · Game Theory and Applications · Experimental Behavioral Economics Studies
