ライティングでは savage competition (しれつな競争) という感じで使えるので、学校やスポーツなどのトピックで以下のように使ってみてください。
The education system's emphasis on standardized testing has created a culture of savage competition among students, prioritizing grades over holistic development and discouraging creativity and collaboration.
The portrayal of violence in media and entertainment has often been criticized for its glamorization of savage behavior, desensitizing audiences to the real-life consequences of such actions.