We prove some interesting properties of unilaterally competitive games when there are more than two players. We show that such games possess: (1) a Nash equilibrium, (2) maximin-solvability, (3) strong solvability in the sense of Nash, and (4) weak acyclicity, all in pure strategies of finite or infinite games.

中文翻译：

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两个以上玩家的单边竞技游戏

当有两个以上玩家时，我们证明了单边竞争游戏的一些有趣特性。我们表明，此类博弈具有：（1）纳什均衡，（2）最大可解性，（3）纳什意义上的强可解性，以及（4）弱非循环性，所有这些都在有限或无限博弈的纯策略中。