Meaning of 鹬蚌相争

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bàng xiāng zhēng (Trad.: 鷸蚌相爭)
lit. sandpiper and clam war together (and the fisherman catches both) (idiom); fig. neighbors who can't agree lose out to a third party
Example Sentences
With skill, Nepal could play one off against the other.
But for property buyers are concerned, it is common snipe mussels competing and profit.
Myanmar's xenophobic leaders are trying to reduce their dependence on China by playing it off against India and the West.
Moreover, in some level, the United States plays a similar one from the off against the profits of the "shot" role.
An old fisherman happened to be walking along the river bank. And without much effort, he captured both the snipe and clam and brought them home.