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THEORY-1199: Real-world games of skill have a spinning-top geometry: their non-transitive part, measured as Nash cluster size, is largest at intermediate strength and narrows toward the strongest and the weakest strategies

1 min read

Properties4
StatusProposed
Tagsgame-theory, learning-theory
SourceLIT-1504 — Real World Games Look Like Spinning Tops
ExtendsTHEORY-930 — In empirical games built from about a thousand sampled search agents in eight OpenSpiel board games, most on 3×3 or 4×4 boards, and in the AlphaStar league, Nash clusters taken from maximum-entropy equilibria are, read against a fitted skew-normal curve with no test, largest at intermediate transitive strength and narrower toward the strongest and the weakest strategies, while Blotto, the disc game, Kuhn poker and noisy Elo games do not show that profile

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Source

Czarnecki, Gidel, Tracey, Tuyls, Omidshafiei, Balduzzi & Jaderberg (2020), LIT-1504, read in full in NOTE-1146 from arXiv:2004.09468v2.

The thesis

Games people play for skill have a transitive axis, from weak to strong, and a non-transitive part that is thickest at middling strength and thin at both ends: a spinning top. The abstract says “We prove the existence of this geometry”; the body withdraws it: “Naturally, the above does not prove that real world games follow the Games of Skill geometry” (p. 6).

What the evidence is

THEORY-930: about a thousand sampled search agents in each of eight small OpenSpiel board games, and the AlphaStar league, with clusters taken from maximum-entropy Nash and a skew-normal curve fitted by eye. The authors say their sampler “does not guarantee uniform sampling of strategies” (p. 9), that the AlphaStar profile reflects “AlphaStar induced game geometry” (p. 18), and that minimum-entropy equilibria would give “more peaky tops” (p. 17).

What this does not say

  • Anything from the theorems. Theorem 1 (THEORY-926) shows long cycles among strategies that can signal, not narrowing at the top.
  • That every game has the shape. Blotto, Kuhn poker and the noisy Elo games do not.

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