Multi-stage equilibrium in electricity pool with flexible ramp market

•Inter-temporal nature of the problem entails application of a dynamic game model.•Uncertainties are tackled by a multi-stage stochastic programming.•A multi-stage stochastic bi-level equilibrium is addressed.•MILP was employed to solve a multi-stage stochastic bi-level equilibrium problem.•Considering another trading market can lead to the existence of equilibrium.