cave in vs show the white flag

cave in

verb
  • To collapse inward or downward. 

  • To relent; to grant approval against one's initial will. 

noun
  • The act of relenting. 

  • The location where something has caved in. 

  • The act of something collapsing or caving in. 

show the white flag

How often have the words cave in and show the white flag occurred in a corpus of books? (source: Google Ngram Viewer )