Games on the Sperner Triangle
<|reference_start|>Games on the Sperner Triangle: We create a new two-player game on the Sperner Triangle based on Sperner's lemma. Our game has simple rules and several desirable properties. First, the game is always certain to have a winner. Second, like many other interesting games such as Hex and Geography, we prove that deciding whether one can win our game is a PSPACE-complete problem. Third, there is an elegant balance in the game such that neither the first nor the second player always has a decisive advantage. We provide a web-based version of the game, playable at: http://cs-people.bu.edu/paithan/spernerGame/ . In addition we propose other games, also based on fixed-point theorems.<|reference_end|>
@article{burke2007games,
    title={Games on the Sperner Triangle},
    author={Kyle Burke and Shang-Hua Teng},
    journal={arXiv preprint arXiv:cs/0702153},
    year={2007},
    archivePrefix={arXiv},
    eprint={cs/0702153},
    primaryClass={cs.GT cs.CC}
}