Internet Mathematics

Atropos: A PSPACE-Complete Sperner Triangle Game

Kyle W. Burke and Shang-Hua Teng

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We create Atropos, a new two-player game based on Sperner's lemma. Our game has simple rules and several desirable properties. First, Atropos is always certain to have a winner. Second, the game is impartial, meaning that both players always can make the same moves. Third, like many other interesting games such as Hex and geography, we prove that deciding whether one can win a game of Atropos is a PSPACE-complete problem. We provide a web-based version of the game, playable at In addition, we propose other games, also based on fixed-point theorems.

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Internet Math., Volume 5, Number 4 (2008), 477-492.

First available in Project Euclid: 1 February 2010

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Burke, Kyle W.; Teng, Shang-Hua. Atropos: A PSPACE-Complete Sperner Triangle Game. Internet Math. 5 (2008), no. 4, 477--492.

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