AI 中文总结
该研究探讨有限博弈的弱非循环性与非循环性，证明弱非循环性等价于优先级规则的非循环性及弱势函数的存在性，完善了博弈均衡可达性的相关理论。
AI 中文摘要
在众多重要的有限博弈族中，纯策略纳什均衡集不仅非空，还可通过一系列近视的单玩家改进或最优反应策略调整，从任意初始策略组合到达。这种弱非循环性弱于博弈的非循环性，后者要求所有此类序列都能到达均衡。例如，所有完美信息扩展式博弈均为弱非循环博弈，但通常并非非循环博弈，因为即使是最优改进步骤序列也可能形成循环。弱非循环性等价于某一优先级规则（仅允许部分改进步的规则）的非循环性，也等价于弱势函数的存在性，弱势函数与普通势函数不同，它仅在部分上述序列上递增而非全部序列。
英文摘要
In a number of large, important families of finite games, not only is the set of pure-strategy Nash equilibria nonempty but it is also reachable from any initial strategy profile by some sequence of myopic single-player moves to a better or best-reply strategy. This weak acyclicity property is weaker than acyclicity of the game, which requires every such sequence to reach an equilibrium. For example, all perfect-information extensive-form games are weakly acyclic, but they are generally not acyclic as even sequences of best-improvement steps may cycle. Weak acyclicity is equivalent to acyclicity of some priority rule, which is a rule that allows only some improvement moves. It is also equivalent to the existence of a weak potential, which unlike a potential increases along some rather than every sequence as above.
