futile game
In game theory, a futile game is a game that permits a draw or a tie when optimal moves are made by both players.{{cite book| last=Steinhaus| first=H.| title=Mathematical Snapshots| edition=3rd| publisher=New York: Dover| year=1999| page=16}}{{cite book |last=Weisstein |first=Eric W. |title=CRC Concise Encyclopedia of Mathematics |publisher=CRC Press |year=2002 |edition=2nd |page=1129}} An example of this type of game is the classical form of Tic-tac-toe,{{Cite book|url=https://books.google.com/books?id=FhWtBAAAQBAJ&dq=example+of+futile+game&pg=PA170|title=Popular Lectures on Mathematical Logic|last=Wang|first=Hao|date=2014-09-22|publisher=Courier Corporation|isbn=9780486171043|language=en}} though not all variants are futile games. The term does not apply to intransitive games, such as iterated prisoner's dilemma or rock–paper–scissors, in which there is no path to a draw or every strategy in the game can be beaten by another strategy.{{Cite book|url=https://books.google.com/books?id=kz0rofjQrwYC&dq=tic+tac+toe+futile+game&pg=PA18|title=Evolutionary Computation for Modeling and Optimization|last=Ashlock|first=Daniel|date=2006-04-04|publisher=Springer Science & Business Media|isbn=9780387319094|language=en}}