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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

Spanish

La estructura y la dinámica de tales sistemas de redes comunitarias pre-organizadas están íntimamente vinculadas. A pesar del inmenso progreso en la caracterización estadística de estos sistemas, un marco mecánico generalizado que explica por qué surgen estructuras mesoscales específicas sigue siendo elusivo. Aquí introducimos el equilibrio de juego-grafo, el punto de descanso estable de una dinámica de pareja-elección orientada a la paga, analógica a un equilibrio de Nash. Esto revela la estructura de la red como el registro fósil de la interacción estratégica. Además, demostramos analíticamente que los juegos de dos tipos complejos tienen exactamente cuatro topologías de red, que son sus exhaustivas fases termodinámicas: asortativa, disortativa y dos periferias de núcleo. Esto genera clases topológicas de

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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