Abstract Various types of inefficiencies of a system state like the Nash equilibrium (NE) exist, such as social inefficiency, Pareto inefficiency, etc. (A system state is inefficient if it is inferior to another realizable state.) Firstly, this article presents a general procedure to obtain each inefficiency measure. The procedure brings as each inefficiency measure, the maximum degree of corresponding inferiority of the state to some other. We examine the procedure in the game-theory context. Vastly-many people use the social-inefficiency measure (represented by the price of anarchy [PoA]). However, it cannot always serve as a Pareto-inefficiency measure. Contrarily, the Pareto-inefficiency measures are yet to establish. Secondly, we follow the procedure (to which PoA also conforms) and obtain Pareto-inefficiency measures. We confirm that they distinguish Pareto inefficiencies that PoA cannot always distinguish. We show a fixed relation between the values of the measures. Further, if a state is proportional to a Pareto-optimal state, proposed measures of strict Pareto inefficiency and Pareto inefficiency behave in identical and straightforward ways. Then, their value is the proportionality constant. Using examples, we examine the measures.

中文翻译：

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低效率的程度

摘要 系统状态存在各种类型的无效率，如纳什均衡（NE），如社会无效率、帕累托无效率等（一个系统状态如果低于另一个可实现状态，则它是无效率的。）首先，本文提出了一个系统状态。获取每个低效率度量的一般程序。程序带来的每一个无效率的措施，相应的国家相对于其他的最大程度的劣势。我们在博弈论的背景下检查程序。很多人使用社会低效率衡量标准（以无政府状态的代价 [PoA] 为代表）。然而，它并不总是作为帕累托无效率的衡量标准。相反，帕累托无效率措施尚未建立。其次，我们遵循程序（PoA 也符合）并获得帕累托无效率测度。我们确认他们区分了 PoA 无法始终区分的帕累托无效率。我们显示了度量值之间的固定关系。此外，如果一个状态与帕累托最优状态成正比，则严格帕累托无效率和帕累托无效率的建议度量以相同且直接的方式表现。那么，它们的值就是比例常数。使用示例，我们检查措施。