<p>This paper investigates the discounted criterion of stochastic Stackelberg games between an energy sharing provider (ESP) and prosumers in a peer-to-peer energy sharing market. The ESP acts as the leader in the Stackelberg game and possesses decision-making priority. As followers, prosumers choose their actions based on the leader’s strategy. The goal of the stochastic Stackelberg game is to maximize the ESP’s reward while minimizing the prosumers’ costs, formulated as a two-level optimization problem in which the objective functions are expressed in terms of an expected discounted criterion with certain interpretations. This model, which has not been previously considered, holds significant application value in smart grids. For any fixed leader’s strategy, the uniqueness of the followers’ best response is essential for determining the Stackelberg equilibrium. This uniqueness is equivalent to that of the optimal strategy in Markov decision processes (MDPs). We study a continuous model characterized by the uniqueness of the optimal strategy in MDPs, where uniqueness is established under convexity and monotonicity conditions. Based on these conditions, the existence of a stochastic Stackelberg equilibrium is proved. The results are illustrated through an analytical example involving stochastic dominance. Furthermore, for cases where uniqueness does not hold, we establish the existence of a stochastic Stackelberg <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\varepsilon \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ε</mi> </math></EquationSource> </InlineEquation>-equilibrium, propose two convergent algorithms, and present a simulation case study to demonstrate their effectiveness.</p>