Game-theoretic learning methods for the vertexcover problem have been investigated in this paper. In thetraditional game theory, the establishment of the game modelis based on the complete objectivity of the players, and theexisting game models describe the vertex cover problem mainlyalong this path. In contrast, this paper considers the impactof players’ subjectivity on decision-making results. First, wepresent a covering game model, where the utility function ofthe player is established under the prospect theory. Then, bypresenting a rounding function, the states of all vertices underNash equilibrium satisfies vertex cover state of a general network. After then, we present a fictitious play distributed algorithm,which can guarantee that the states of all vertices converge aNash equilibrium. Finally, the simulation results are presentedto assess the impact of players’ subjectivity on the overall coverresults of networks.