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Bibliographische Detailangaben
1. Verfasser:	Fathi, Kevin
Format:	Recurso digital
Sprache:	Englisch
Veröffentlicht:	Zenodo 2025
Schlagworte:	Cooperative Game Theory Core Stability Principle of Geometric Balance (PGB) Bondareva-Shapley Theorem Harsanyi Dividends Canonical Localization L-GCAS (Local G-CAS) G-CAS (Globally Canonically Antagonistic Structure) Aggregated Canonical Testers Canonical Ramsey Theorem Erdős-Rado Theorem Network-Generated Games (NGGs) Cross-Coalition Synergy
Online-Zugang:	https://doi.org/10.5281/zenodo.17596085
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Inhaltsangabe:

The Principle of Geometric Balance (PGB) posits: asymptotically, a cooperative game has a non-empty core if and only if it contains no Globally Canonically Antagonistic Structure (G–CAS). This paper provides a complete and unified formal development of the necessity direction (Empty Core ⇒ G–CAS), merging and reconciling earlier routes. (I) Route C1 and the Generator. We derive the exact triangular decomposition of any size-symmetric Bondareva–Shapley (B–S) functional into aggregated canonical testers bbk. We then prove unconditionally that the associated coefficients γk are nonnegative (the Generator Property), via an LP extreme-point reduction and exact combinatorial identities (a Beta-function identity and subset-of-a-subset factorization). This settles the generator gap and implies that any global violation yields a positive canonical deficit in some size k (an L–GCAS). (II) Canonical localization. Using a quantitative canonicalization lemma (via Erd˝os– Rado canonical Ramsey), we upgrade a positive expectation margin to an explicit canonical witness P with Fk(P ) > 0. (III) Minimax orbit smoothing and finite reductions. We formalize orbit averag- ing, the size-symmetric subspace, exact formulas for layer-uniform witnesses, and a conic Carath´eodory reduction that yields few-size canonical certificates. (IV) Limits of globalization and structured regimes. We prove a model-free No- Go theorem: internal dividends of P cannot universally bound cross-capacity S(P ; N \ P ). Consequently, L–to–G globalization requires structure. We then fully prove PGB necessity in two regimes providing such structure: (a) network-generated games with rapid attenuation (Strong Localization) and (b) bounded cross-capacity with a magnitude-aware tradeoff.

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