Cannibal Animal Games: a new variant of Tic-Tac-Toe

This paper presents a new partial two-player game, called the 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 wins if she occupies a set of cells, the union of a subset of which is a translated or rotated copy of a previously agreed upon polyomino P (called an animal). The objective of the second player Bob is to prevent Alice from creating her animal by occupying in each round a translated or rotated copy of P . An animal is a cannibal if Bob has a winning strategy, and a non-cannibal otherwise. This paper presents some new tools, such as the bounding strategy and the punching lemma, to classify animals into cannibals or non-cannibals, It is also shown that the pairing strategy also works for this problem.