<p>Static games on networks are often analyzed under well-mixed assumptions, yet in many socio-technical and biological systems the interaction topology strongly shapes both transient dynamics and long-run strategic outcomes. Motivated by this gap, we conduct agent-based simulations of four complete-information static games (Prisoner’s Dilemma, Hawk–Dove, Stag Hunt, and Public Goods) on six network families (Erdős–Rényi, Barabási–Albert, Watts–Strogatz, complete, degree-homogeneous random regular, and LFR community graphs). We compare multiple strategy update mechanisms implemented in our simulator (population-sampling replicator, Moran birth–death, pairwise imitation (Fermi-like), stochastic best-response, unconditional imitation, and a probabilistic Tit-for-Tat variant). For each game–network–update combination, we report (i) the fraction of cooperative actions (strategy = 1) over time, (ii) the time (in simulation steps) to reach an absorbing configuration, and (iii) a proxy equilibrium count computed from the final strategy profile. Across our parameterization, highly connected graphs consistently reduce convergence time, while cooperation levels are primarily driven by the update mechanism and payoff structure; in particular, the probabilistic Tit-for-Tat variant yields near-universal cooperation across all tested topologies, whereas Moran and replicator-type updates exhibit topology- and game-dependent cooperation. We discuss how these findings relate to classic results that increased degree can hinder cooperation in standard payoff settings, and we clarify the methodological limits of our proxy equilibrium metric. The presented framework provides a reproducible baseline for systematic cross-factor comparison of topology, payoff design, and learning dynamics in networked strategic systems.</p>