By dynamic game theory for the repeated auction in electricity markets， the stability， uniqueness and convergence of the pure Nash equilibrium in Pool-based electricity markets are analyzed with the Betrand game model. And the electricity price is used to be the reference variable. The stability of the equilibrium depends on the power capacity must run ratio（MRR） and the number of the equilibrium points decided by MRR. When there is only one equilibrium point， the equilibrium is stable; when a lot of equilibrium points appear， the stability relates to the original state. Global stability， regional stability， stochastic state and equivalent marginal cost are presented. And these results are also illuminated with examples.