This article addresses the challenges of load curve variability in integrated energy systems (IES) and emphasizes carbon neutralization in response to global environmental concerns. It introduces a game-theoretic approach to understand the collaborative dynamics within an integrated energy-hydrogen system (HGESS). The study develops a collaborative game model for the IES-HGESS partnership, focusing on carbon neutralization considerations. Using game theory, it investigates the determinants shaping this partnership and extends to create a hybrid model for day-ahead and real-time markets. To foster enduring cooperation, the study introduces a cooperation profit coefficient and devises an income distribution strategy for HGESS-IES interactions. A load management program is incorporated to reduce costs and enhance profitability. Addressing complexity and constraints, the article introduces an advanced multi-objective particle swarm optimization method. Tested on a sample system under various conditions, the results demonstrate that the alliance between IES and HGESS can significantly enhance net profits, achieving mutual benefit and a win-win outcome while advancing sustainability in energy management.