rivalry vs tug of war

rivalry

noun
  • Any competition between two or more things or factors. 

  • The characteristic of being a rivalrous good, such that it can be consumed or used by only one person at a time. 

  • An ongoing relationship between (usually two) rivals who compete for superiority. 

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 rivalry and tug of war occurred in a corpus of books? (source: Google Ngram Viewer )