Sperner Triangle上的游戏
Games on the Sperner Triangle
摘要：
基于Sperner引理，我们在Sperner三角形上创建了一个新的两人博弈。我们的游戏有简单的规则和几个理想的属性。首先，游戏总是有赢家。其次，像许多其他有趣的游戏，如十六进制和地理，我们证明，决定是否可以赢得我们的游戏是一个PSPACE完全问题。第三，游戏中有一个优雅的平衡，第一个和第二个玩家都不总是具有决定性的优势。我们提供了一个基于网络的游戏版本，可在：http://cs-people.bu.edu/paithan/spernerGame/。此外，我们还提出了其他同样基于不动点定理的游戏。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
