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The integration of source-grid-load-storage greatly improves the energy managing flexibility of regional integrated energy systems (RIES). Considering the conflicting interests of multi-operator, this paper divides RIES into 1) energy supply center (ESC); 2) load aggregator (LA); 3) energy storage aggregator (ESA), and establishes a multi-operator two-layer optimal scheduling model by combining 1) the Stackelbelberg-Nash asymmetric bargaining game based on the genetic algorithm; and 2) the alternating direction method of multipliers algorithm (GA-ADMM). Firstly, considering the absence of historical data, trapezoidal fuzzy parameters are introduced to construct fuzzy chance constraints based on credibility theory to simulate the source-load uncertainties. Secondly, the uncertainty of demand response behavior, real-time carbon credits trading within RIES, and cooperation-competition behavior of followers (LA and ESA) are considered to simulate the asymmetric relationship between followers and leaders (ESC) based on GA. Then, based on the ADMM algorithm, a Nash asymmetric bargaining game considering energy dependency and energy supply-reception status is proposed to realize the revenue allocation between followers. Finally, simulations are implemented to verify the validity and reliability of the proposed model. Results show that: 1) Cooperation improves the energy-managing flexibility of followers, reduces their dependence on ESC, and thus enhances their game ability. 2) The real-time carbon credits trading enables zero-carbon energy interactions and natural gas replenishment within RIES. 3) Increases in the price of various energy and carbon credits can enhance cooperation between followers. • Source-load uncertainties are considered by FCCP. • Regional carbon credits trading based on sharing CCS is established. • The asymmetric game relationship of multi-operator is simulated. • A revenue allocation considering consumption features and efficiency is proposed. • The stability of followers' competition-cooperation relationship is explored. [ABSTRACT FROM AUTHOR]