Abstract Integrated energy systems (IESs) as the widely concerned multi-energy systems have significant contributions to enhancing energy utilization efficiency and renewable energy (RE) consumption. With the increasing proportion of RE, integrated energy aggregators (IEAs), who coordinate IESs with multiple generators, will have more important roles in the future smart grid. This paper presents a Bayesian evolutionary game (BEG) method to study the optimal supply strategy for generating units of different energy types to maximize their own profits in an unregulated power market. The competition among IEAs lowers their willingness to share their information and restricts the profit themselves. Given this information asymmetry, the interaction of three types of generators in IESs is captured by the Bayesian game to transform the incomplete game into a complete game with imperfect information. Given the dynamic of the spot market, this paper combines the Evolutionary game theory with Bayesian theory to study the symbiotic evolution among them. Simulations are introduced to examine the asymptotic stability of various evolutionary stabilization strategies. The results verify the effectiveness of the proposed model. Finally, the implications of different renewable energy penetration, market-clearing rules, market share, and the market supply-demand ratio on IEAs’ offering behavior are explored by applying the experimental economics principle.