It is a significant and challenging problem to coordinate multiple microgrids (MMGs) belonging to different entities and achieve their excellent energy-sharing performance to ensure the stability of electricity markets. This article studies a grid-oriented energy bidding problem for MMGs with peer-to-peer (P2P) energy trading under uncertainty. A stochastic Cartel game (SCG) based strategy is developed. A stochastic Cartel nonlinear programming model is formulated to characterize the joint energy bidding, the energy production, and P2P energy transactions while minimizing the total cost for MMGs under uncertainty. A diagonal quadratic approximation method is employed to linearize quadratic terms, and the SCG problem for MMGs is further decomposed into subproblems for individual MGs based on a surrogate Lagrangian relaxation method. The equivalence of problem transformation is proved and equilibrium solutions are derived in an iterative and distributed manner. Comparisons for different strategies, models, and solution algorithms are conducted to testify the rationality and validity of the proposed strategy.