During the Warring States Period, the states of Han and Wei fought for over a year but still could not agree which side was victorious. Emperor Qin wanted to dispatch troops to intervene, so he convened his ministers to discuss the problem. Unfortunately, their opinions differed greatly and proved to be of little help to Emperor Qin.
Chen Zhen, in the State of Chu, heard about the Emperor's problem and so shared the story of Bian Zhuangzi and the tigers, "Once, Bian Zhuangzi saw two tigers who'd caught an ox. He wanted to kill the tigers, but a waiter stopped him, saying, 'Now the two tigers are eating beef. They must fight for the food. After they fight, the tiger with less strength will be killed and the other one will be injured. This is the best time to kill the injured tiger.'".
Bian Zhuangzi felt the waiter had a good point, so he stood to the side and watched the fight unfold. As expected, one tiger was killed, while the other was injured. He happily killed the injured one.
This story uses the two tigers as a metaphor for the State of Han and Wei. By telling it Chen Zhen was suggesting that for the greatest benefit Emperor Qin should dispatch troops only when both States were weak from long-term fighting. Emperor Qin happily adopted his suggestion.
"两败俱伤"means a fight in which neither side benefits, but rather both sides are mutual injured, "俱" means both.
例句:
1、在国内和他们公司这样竞争下去,必定会两败俱伤。我们不如去开发海外的市场。 It we continue to compete with this domestic company, we'll end up hurting each other and failing. Why not explore the market overseas instead?
2、两国人民都因为战争而生活困苦,所以没有真正的赢家,战争只会让人两败俱伤。 People in both countries suffered because of the war. In the end there's no real winner. The war resulted in mutual destruction.