Cannibal Animal Games: a new variant of TicTacToe
Abstract
This paper presents a new partial twoplayer game, called the \emph{cannibal animal game}, which is a variant of TicTacToe. 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{noncannibal} otherwise. This paper presents some new tools, such as the \emph{bounding strategy} and the \emph{punching lemma}, to classify animals into cannibals or noncannibals. We also show that the \emph{pairing strategy} works for this problem.
 Publication:

arXiv eprints
 Pub Date:
 June 2013
 arXiv:
 arXiv:1306.4884
 Bibcode:
 2013arXiv1306.4884C
 Keywords:

 Computer Science  Computer Science and Game Theory