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Strategic Origins of Network Structure

Christoph Riedl, Rory Smead · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.24792 · cited by 0 works (OpenAlex) · open-access PDF

Korean

이러한 공동체 네트워크의 기계와 역학은 밀접하게 연관되어 있습니다. 이러한 시스템을 통계적으로 특징화하는 엄청난 프레임에도 불구하고, 특정 mesoscale 구조가 나타나는 이유를 설명하는 일반적인 기계적 프레임은 여전히 까다롭습니다. 여기서 우리는 게임 그래프 균형을 소개합니다. payoff-driven 파트너 선택의 안정적인 휴식 지점, Nash 균형과 유사한 두 개의 핵심 역학. 이것은 전략적 상호 작용의 화석화 된 기록으로 네트워크 구조를 공개합니다. 우리는 분석적으로 두 가지 유형의 게임이 정확히 네트워크 토폴로지를 가지고 있음을 증명합니다. 그들의 광범위한 열대 역학적 단계는 : assortative, disassortative, 두 개의 핵

Machine translation (Meta M2M100); the English original follows.

Abstract

The structure and dynamics of complex networks are intimately linked. Despite immense progress in statistically characterizing these systems, a generalized mechanistic framework explaining why specific mesoscale structures emerge remains elusive. Here we introduce the game-graph equilibrium, the stable rest point of a payoff-driven partner-choice dynamic, analogous to a Nash equilibrium. This reveals network structure as the fossilized record of strategic interaction. We prove analytically that two-type games have exactly four network topologies, which are their exhaustive thermodynamic phases: assortative, disassortative, and two core-peripheries. This result generalizes to $K^K$ topological classes for $K$-type interactions. Furthermore, four distinct Nash equilibria produce core-periphery topologies, yet their payoffs reveal whether the underlying dynamic is cooperative or exploitative. To recover the generating dynamics from observed networks, we develop mechanistic inference by constraining a block model to lie on a low-dimensional, game-theoretic manifold. Applied to real-world networks, the model yields interpretable quantities, distinguishes states that look identical to conventional methods, predicts network topologies it has never seen without retraining, and controls its own complexity without hand-tuned penalties. Networks such as international trade are well described by the model despite the hard constraint, suggesting that real-world systems are organized by payoff-driven partner choice. Our framework resolves a foundational ambiguity by offering a precise, mechanistic definition of communities: strategic equivalence.

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Topics: Ambiguity, Nash equilibrium, Computer science, Inference, Network structure, Network formation

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