Chomp is a two-player game played with a bar of chocolate which is divided
into an m by n grid of pieces. The two players take turns: the current
player must choose a block of chocolate remaining in the bar, and eat
that block, along with all blocks that are below or to the right of the
chosen block (or both below and to the right). The player who finishes the
chocolate bar (or equivalently, eats the piece in the upper-left corner) loses.
Now, imagine ordinal chomp, where the dimensions of the chocolate bars can
be ordinals. Let's specifically consider the 2D infinite chocolate bar ω × ω
(that is, the bar stretches infinitely down and to the right). Is there
any way that the two players could conspire to make the game last forever?
Is there a winning strategy for either player?