This paper presents a new partial two-player game, called the \emph{ cannibal animal game}, which is a variant of Tic-Tac-Toe. The game is played on the infinite grid, where in each round a player chooses and occupies free cells. The first player Alice can occupy a cell in each turn and wins if she occupies a set of cells, the union of a subset of which is a translated, reflected and/or rotated copy of a previously agreed upon polyomino $P$ (called an \emph{ animal}). The objective of the second player Bob is to prevent Alice from creating her animal by occupying in each round a translated, reflected and/or rotated copy of $P$. An animal is a \emph{ cannibal} if Bob has a winning strategy, and a \emph{ non-cannibal} otherwise. This paper presents some new tools, such as the \emph{ bounding strategy} and the \emph{ punching lemma}, to classify animals into cannibals or non-cannibals. We also show that the \emph{ pairing strategy} works for this problem.
Categories: cs.GT