Distributed decision-making in a shared power network: a game-theoretic framework for integrated electricity and gas systems

With the advancement of power-to-gas (P2G) technology and local energy markets, new opportunities emerge for small-scale gas distributors (GDs) to unlock additional value. However, research on multiple GDs within the same power network participating in local energy markets remains unexplored, potentially leading to suboptimal collaborative efficiency and market imbalance. To bridge this gap, this paper proposes a heterogeneous game framework that integrates mixed-integer Nash equilibrium problem (MI-NEP) and generalized Nash equilibrium problem (GNEP). The framework assumes rational GDs simultaneously engage in non-convex GNEP for optimal power flow (OPF) coordination in distribution systems while addressing MI-NEP governing pipeline flow control in local gas market transactions. We develop a collaborative computing solution combining the best response (BR) method with a Korpelevich-inspired algorithm to obtain Nash equilibrium (NE) solutions ensuring fairness and operational stability. Comprehensive case studies on integrated 10-node power distribution networks with 7-node and 20-node gas networks demonstrate that the algorithm converges within 10 iterations with a residual error below [Formula: see text]. The proposed framework effectively ensures market fairness by reducing the cost disparity between isomorphic agents to zero.