True exhibition games between opposing colleges at the highest level do not exist in college football; due to the importance of opinion polling in the top level of college football, even exhibition games would not truly be exhibitions because they could influence the opinions of those polled. Intramural games are possible because a team playing against itself leaves little ability for poll participants to make judgments, and at levels below the Football Bowl Subdivision (FBS), championships are decided by objective formulas and thus those teams can play non-league games without affecting their playoff hopes.
What is a game called in which a team plays against another team? (If the question is unanswerable, say "unanswerable")
unanswerable