A PSPACE-complete Sperner triangle game

Authors:
Kyle W. Burke;Shang-Hua Teng
Affiliations:
Boston University;Boston University
Venue:
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Year:
2007

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Abstract

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.