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This paper proposes a distributed algorithm for games with shared coupling constraints based on the variational approach and the proximal-point algorithm. The paper demonstrates the effectiveness of the proximal-point algorithm in distributed computing of generalized Nash equilibrium (GNE) problems using local data and communication with neighbors in any networked game. The algorithm achieves the goal of reflecting local decisions in the Nash–Cournot game under partial-decision information while maintaining the distributed nature and convergence of the algorithm.