We define and investigate a novel notion of expressiveness for temporal logics that is based on game theoretic equilibria of multi-agent systems. We use iterated Boolean games as our abstract model of multi-agent systems [Gutierrez et al. 2013, 2015a]. In such a game, each agent has a goal , represented using (a fragment of) Linear Temporal Logic ( ) . The goal captures agent ’s preferences, in the sense that the models of represent system behaviours that would satisfy . Each player controls a subset of Boolean variables , and at each round in the game, player is at liberty to choose values for variables in any way that she sees fit. Play continues for an infinite sequence of rounds, and so as players act they collectively trace out a model for , which for every player will either satisfy or fail to satisfy their goal. Players are assumed to act strategically, taking into account the goals of other players, in an attempt to bring about computations satisfying their goal. In this setting, we apply the standard game-theoretic concept of (pure) Nash equilibria. The (possibly empty) set of Nash equilibria of an iterated Boolean game can be understood as inducing a set of computations, each computation representing one way the system could evolve if players chose strategies that together constitute a Nash equilibrium. Such a set of equilibrium computations expresses a temporal property—which may or may not be expressible within a particular fragment. The new notion of expressiveness that we formally define and investigate is then as follows: What temporal properties are characterised by the Nash equilibria of games in which agent goals are expressed in specific fragments of ? We formally define and investigate this notion of expressiveness for a range of fragments. For example, a very natural question is the following: Suppose we have an iterated Boolean game in which every goal is represented using a particular fragment of : is it then always the case that the equilibria of the game can be characterised within ? We show that this is not true in general.

中文翻译：

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迭代布尔游戏中的表现力和纳什均衡

我们定义并研究了一种基于多智能体系统博弈论均衡的时间逻辑表达性的新概念。我们用迭代布尔游戏作为我们的多智能体系统的抽象模型 [Gutierrez 等人。2013, 2015a]。在这样的博弈中，每个代理 有一个目标 ，用（的片段）表示线性时序逻辑 ( ). 目标 捕获代理 的偏好，在某种意义上， 表示满足的系统行为 . 每个玩家控制一个布尔变量的子集 ，并且在游戏的每一轮中，玩家 可以自由选择变量的值 以她认为合适的任何方式。游戏会持续进行无限轮次，因此当玩家行动时，他们会共同找出一个模型 ，对于每个玩家来说，要么满足要么不能满足他们的目标。假设玩家采取战略行动，考虑到其他玩家的目标，以尝试实现满足他们目标的计算。在这种情况下，我们应用了（纯）纳什均衡的标准博弈论概念。迭代布尔博弈的纳什均衡（可能是空的）集合可以理解为引发一组计算，如果参与者选择共同构成纳什均衡的策略，每个计算代表系统可能进化的一种方式。这样的一组平衡计算表达了一种时间属性——它可能在一个特定的 分段。我们正式定义和研究的新的表现力概念如下：纳什均衡博弈的特点是什么时间属性，其中代理目标以特定的片段表示 ? 我们正式定义并研究了这种表达性概念，适用于一系列 碎片。例如，一个非常自然的问题如下：假设我们有一个迭代的布尔游戏，其中每个目标都用一个特定的片段来表示 的 : 那么博弈的均衡是否总是可以在 ?我们表明，这通常是不正确的。