News-driven time series forecasting (NTSF) uses evolving textual events together with historical observations to predict future values, supporting applications such as market risk monitoring and resource scheduling. In multi-agent settings, two challenges still remain. The first is degeneration of thought, where agents converge to similar evidence-seeking behaviors. The second is insufficient theoretical grounding, where strategy updates are often heuristic and lack a principled formulation. To address the above challenges, we propose CompEvo, a competition-induced evolution framework for multi-agent NTSF. At the theoretical level, our evolutionary game formulation establishes equilibrium existence and local convergence under the stated assumptions. At the methodological level, we construct a trainable multi-agent evolution framework that integrates strategy execution, fitness-based differentiable selection, and competition-induced strategy evolution. CompEvo enables heterogeneous agents to explore diverse news evidence, converts forecasting feedback into differentiable influence weights, and evolves agent strategies under competitive pressure to preserve effective logic while maintaining diversity. Experiments on four real-world datasets show that CompEvo reduces RMSE by 29.8% and MAPE by 30.3% on average relative to the strongest multi-agent baseline. Further analysis indicates that CompEvo maintains diverse and specialized agent behaviors.