Open Access
2008 Atropos: A PSPACE-Complete Sperner Triangle Game
Kyle W. Burke, Shang-Hua Teng
Internet Math. 5(4): 477-492 (2008).


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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Kyle W. Burke. Shang-Hua Teng. "Atropos: A PSPACE-Complete Sperner Triangle Game." Internet Math. 5 (4) 477 - 492, 2008.


Published: 2008
First available in Project Euclid: 1 February 2010

zbMATH: 1194.91025
MathSciNet: MR2604973

Rights: Copyright © 2008 A K Peters, Ltd.

Vol.5 • No. 4 • 2008
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