It is played by two players on a given set S of positive real numbers.
Without loss of generality, assume player A chooses the larger number, so x ≥ y.
Then the payoff to A is 0 if x = y, 1 if 1 < x/y < T and −ν if x/y ≥ T. Thus each player seeks to choose the larger number, but there is a penalty of ν for choosing too large a number.
A large number of variants have been studied, where the set S may be finite, countable, or uncountable.
Extensions allow the two players to choose from different sets, such as the odd and even integers.