Newest papers

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

Portuguese

A estrutura e a dinâmica de tais sistemas de rede comunitários são intimamente ligados. Apesar do imenso progresso na caracterização estatística desses sistemas, um quadro mecânico generalizado que explica por que estruturas mesoscales específicas surgem permanece elusivo. Aqui apresentamos o equilíbrio do jogo-grafo, o ponto de descanso estável de uma dinâmica de escolha de parceiros orientada por pagamento, analógica a um equilíbrio de Nash. Isto revela a estrutura da rede como o registro fossilizado de interações estratégicas. Além disso, demonstramos analiticamente que os nossos jogos de dois tipos complexos têm exatamente quatro topologias de rede, que são suas fases termodinâmicas exaustivas: assortativa, disassortativa e duas periferias de núcleo. Isso resulta em classes topológicas

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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