From Identification to Obfuscation: A Survey of Cross-Network Mapping and Anti-Mapping Methods

User identity linkage (UIL) across online social networks seeks to match accounts belonging to the same real-world individual. This cross-platform mapping enables accurate user modeling but also raises serious privacy risks. Over the past decade, the research community has developed a wide range of UIL methods, from structural embeddings to multimodal fusion architectures. However, corresponding adversarial and defensive approaches remain fragmented and comparatively understudied. In this survey, we provide a unified overview of both mapping and anti-mapping methods for UIL. We categorize representative mapping models by learning paradigm and data modality, and systematically compare them with emerging countermeasures including adversarial injection, structural perturbation, and identity obfuscation. To bridge these two threads, we introduce a modality-oriented taxonomy and a formal game-theoretic framing that casts cross-network mapping as a contest between mappers and anti-mappers. This framing allows us to construct a cross-modality dependency matrix, which reveals structural information as the most contested signal, identifies node injection as the most robust defensive strategy, and points to multimodal integration as a promising direction. Our survey underscores the need for balanced, privacy-preserving identity inference and provides a foundation for future research on the adversarial dynamics of social identity mapping and defense.