With their prominent scene understanding and reasoning capabilities, pre-trained visual-language models (VLMs) such as GPT-4V have attracted increasing attention in robotic task planning. Compared with traditional task planning strategies, VLMs are strong in multimodal information parsing and code generation and show remarkable efficiency. Although VLMs demonstrate great potential in robotic task planning, they suffer from challenges like hallucination, semantic complexity, and limited context. To handle such issues, this paper proposes a multi-agent framework, i.e., GameVLM, to enhance the decision-making process in robotic task planning. In this study, VLM-based decision and expert agents are presented to conduct the task planning. Specifically, decision agents are used to plan the task, and the expert agent is employed to evaluate these task plans. Zero-sum game theory is introduced to resolve inconsistencies among different agents and determine the optimal solution. Experimental results on real robots demonstrate the efficacy of the proposed framework, with an average success rate of 83.3%.