Monotonic Sequence Games
  In a monotonic sequence game, two players alternately choose elements of a sequence from some fixed ordered set. The game ends when the resulting sequence contains either an ascending subsequence of length a or a descending one of length d. We investigate the behaviour of this game when played on finite linear orders or Q and provide some general observations for play on arbitrary ordered sets. 
M. Albert, R. Aldred, M. Atkinson, C. Handley, D. Holton, D.   McCaughan, and B. Sagan