A number of information and resource sharing systems arise and become popular with the rapid development of communication technologies and mobile smart devices. The interactions between humans and machines are intense and their synergistic reactions have attracted special attention for the reason of forming so called Human-Machine Networks (HMN). HMNs refer to these networks where humans and machines work together to provide synergistic effects on their payoffs. Game theory, which can capture the interactions among players dexterously, has been widely used in solving various problems in HMN systems from the view of economics. In this paper, we extensively review the literature about game theoretical methods in HMNs, in particular focusing on its typical systems such as crowdsourcing, an elemental HMN and Internet of Things (IoT), a hybrid HMN, as well as Bitcoin. We propose a series of requirements to evaluate existing work. For reviewing and analyzing each system, we specify application purposes, players, strategies, game models and equilibria based on our proposed requirements. In the sequel, we identify a number of common and distinct open issues in HMNs and point out future research directions.