Analyzing demand in environments with incomplete information is a challenging task. This paper proposes a novel agent-based Pythagorean fuzzy approach for analyzing this kind of demand. First, a Bayesian game is described with a large number of finite players, and this is followed by a Pythagorean fuzzy-based decision mechanism. Unlike the classical methods in the literature, the proposed method in this paper neither assumes nor forecasts the demand in a system. Instead, it tries to analyze the demand when there is limited availability of input data, or processing data are computationally expensive. The study ends with an application of the proposed system to an electricity grid. Electricity prices used as an incentive to construct an agent-based system that efficiently reduces the peak amounts in a smart grid by analyzing the demand. Test results provide evidence that the proposed approach is promising to design demand response systems.