This volume constitutes the refereed proceedings of 18th International Symposium on Algorithmic Game Theory, SAGT 2025, held in Bath, UK, during September 2–5, 2025.The 26 full papers included in this book were carefully reviewed and selected from 68 submissions. They were organized in topical sections as follows:Computational and Algorithmic Aspects of Games; Facility Location; Fair Division and Resource Allocation; Markets and Matching; Bayesian Decision Making; Mechanism Design and Algorithmic Contracts and Computational Social Choice.