Lukasiewicz logics for cooperative games
Lukasiewicz logics for cooperative games
复制标题
合作博弈的 Lukasiewicz 逻辑
DOI：
10.1016/j.artint.2019.03.003
复制
发表时间：
2019
影响因子：
14.4
通讯作者：
Marchioni E
中科院分区：
文献类型：
--
作者：
Marchioni E
联盟资源博弈（CRG）提供了一个自然的抽象框架，在该框架中，一组代理通过共享资源进行合作，以执行任务或实现个人目标。在这项工作中，我们介绍了一个更丰富和更一般的框架，称为Eukasiewicz资源游戏（Eukasiewicz RG），这是基于多值Eukasiewicz逻辑，其公式使得有可能指定的整数和有理系数的分段线性多项式函数类在[0，1] n。Łukasiewicz逻辑的使用为CRG建模的场景/情况的表示提供了一种新的方法。在EARRGs中，每个代理都被赋予了资源，可以分配给一组任务，其中任务的结果取决于配置文件的资源分配给它。我们指定的任务结果使用公式的EARukasiewicz逻辑。此外，代理人有支付功能的任务成果，这也是指定的Eschukasiewicz公式。在激励和介绍了EARRGs之后，我们正式定义了EARRGs的联盟结构和核心概念，并从逻辑和计算的角度研究了核心的非空性。我们证明，CRG是一个适当的概括CRG显示任何CRG可以被翻译成一个CRG是战略上等价的，在这个意义上说，前者有一个非空的核心，当且仅当这样做，后者。
Coalitional resource games (CRGs) provide a natural abstract framework with which to model scenarios in which groups of agents cooperate by pooling resources in order to carry out tasks or achieve individual goals. In this work, we introduce a richer and more general framework, called Łukasiewicz resource games (ŁRG), which is based on many-valued Łukasiewicz logics, whose formulae make it possible to specify the class of piecewise linear polynomial functions with integer and rational coefficients on [0, 1] n. The use of Łukasiewicz logics provides a new approach to the representation of the scenario/situations modelled by CRGs. In ŁRGs, each agent is endowed with resources that can be allocated over a set of tasks, where the outcome of a task depends on the profile of resources that are allocated to it. We specify task outcomes using formulae of Łukasiewicz logic. In addition, agents have payoff functions over task outcomes, which are also specified by Łukasiewicz formulae. After motivating and introducing ŁRGs, we formalise notions of coalition structures and the core for ŁRGs and investigate the non-emptiness of the core both from a logical and computational perspective. We prove that ŁRGs are a proper generalisation of CRGs by showing how any CRG can be translated into a ŁRG that is strategically equivalent, in the sense that the former has a non-empty core if and only if so does the latter.