Careful rational synthesis was defined in (Condurache et al. 2021) as a quantitative extension of Fisman et al.'s rational synthesis (Fisman et al. 2010), as a model of multi-agent systems in which agents are interacting in a graph arena in a turn-based fashion. There is one common resource, and each action may decrease or increase the resource. Each agent has a temporal qualitative objective and wants to maintain the value of the resource positive. One must find a Nash equilibrium. This problem is decidable. In more practical settings, the verification of the critical properties of multi-agent systems calls for models with many resources. Indeed, agents and robots consume and produce more than one type of resource: electric energy, fuel, raw material, manufactured goods, etc. We thus explore the problem of careful rational synthesis with several resources. We show that the problem is undecidable. We then propose a variant with bounded resources, motivated by the observation that in practical settings, the storage of resources is limited. We show that the problem becomes decidable, and is no harder than controller synthesis with Linear-time Temporal Logic objectives.
翻译:在(Condurache等人,2021年)中,审慎的合成被定义为Fisman等人的理性合成(Fisman等人,2010年)的定量扩展(Fisman等人,2010年),作为多试剂系统的一种模型,在其中,各种物剂在图形舞台上以转动方式相互作用。有一个共同的资源,每个行动都可能减少或增加资源。每种物剂都有一个时间质量目标,希望保持资源正值。必须找到纳什平衡。这个问题是可以改变的。在更实际的环境下,多试剂系统的关键特性的核查需要多种资源的模型。事实上,物剂和机器人消费和生产一种以上类型的资源:电能、燃料、原材料、制成品等。因此,我们探索了与若干资源进行仔细合理合成的问题。我们表明,这个问题是不可估量的。我们随后提出了一个受实际环境下资源储存有限这一观察驱动的、与资源捆绑在一起的变体的变体。我们发现,问题变得容易分解,而且没有比控制器与线形逻辑目标更难。