Internet Mathematics

Atropos: A PSPACE-Complete Sperner Triangle Game

Kyle W. Burke and Shang-Hua Teng

Full-text: Open access

Abstract

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 http://cs-people.bu.edu/paithan/atropos/. In addition, we propose other games, also based on fixed-point theorems.

Article information

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

Dates
First available in Project Euclid: 1 February 2010

Permanent link to this document
https://projecteuclid.org/euclid.im/1265033176

Mathematical Reviews number (MathSciNet)
MR2604973

Zentralblatt MATH identifier
1194.91025

Citation

Burke, Kyle W.; Teng, Shang-Hua. Atropos: A PSPACE-Complete Sperner Triangle Game. Internet Math. 5 (2008), no. 4, 477--492. https://projecteuclid.org/euclid.im/1265033176


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