War of Attrition

From Encyc

A war of attrition is a type of warfare in which the outcome is decided by which side takes greater casualties and runs out of manpower first. The latter parts of the American Civil War and World War I were wars of attrition.

The most famous example is Pyrrhus of Epirus and his war against Rome. He won on the battlefield, but lost so many men that he was forced to withdraw.