تأثير درجه‌ي رأس بر ديناميك كاوش و تقليد در شبكه‌هاي پيچيده

Motivated by Social Learning Theory an‎d prestige-biased transmission (where high-status individuals attract greater attention an‎d exert stronger influence on potential imitators) we study exploration-‎-imitation dynamics of continuous strategies on networks, using vertex degree as a minimal proxy for both visibility (being selec‎ted as a role model) an‎d imitation strength (effective influence). Building on the analytical baseline, we perform agent-based simulations on several canonical network models. In the baseline model, each agent selec‎ts a neighbor uniformly at ran‎dom an‎d updat‎es its strategy as a combination of its previous state, the chosen neighbor’s state with constant imitation strength α, an‎d a stochastic exploration term. Exploration represents exogenous information an‎d intrinsic behavioral fluctuations, which broaden the strategy distribution, while soft imitation counteracts this tendency by reducing dispersion; the competition between these mechanisms leads to a nontrivial steady-state variance. In the extended models, degree effects are introduced in two distinct ways: (i) by biasing role-model selec‎tion toward high-degree neighbors, an‎d (ii) by making imitation strength explicitly degree-dependent. A fourth model incorporates both mechanisms simultaneously. To obtain statistically reliable estimates, each network realization is simulated multiple times an‎d ensemble averages together with stan‎dard errors are reported; moreover, to disentangle dynamical effects from structural ran‎domness, the same generated network realization is used across all four models. Our results show that, except for the well-mixed case, the considered networks are approximately matched in average degree, yet they produce markedly different stationary dispersions: networks with higher clustering an‎d especially larger average shortest-path length exhibit larger steady-state variance. For Watts-‎-Strogatz networks, the variance displays an initial transient dip before converging to its stationary value, an‎d the dip depth is found to be inversely related to the algebraic connectivity of the network. Finally, for Barabʹasi-‎-Albert networks an‎d for a range of the construction parameter m, the relative steady-state variance gap between the degree-dependent imitation model an‎d the baseline model follows an exponential decay as m increases.

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فرهاد شهبازي دستجرده

فرهاد فضيله , اسماعيل عبدالحسيني سارسري