competition vs tug of war

competition

noun
  • The competitors in such a contest. 

  • A contest for a prize or award. 

  • The action of competing. 

tug of war

noun
  • A game or competition in which two teams pull or tug on opposite ends of a rope trying to force the other team over the line which initially marked the middle between the two teams. 

  • A dispute between two parties, particularly an entrenched, back-and-forth dispute. 

How often have the words competition and tug of war occurred in a corpus of books? (source: Google Ngram Viewer )