Watermarking Game-Playing Agents in Perfect-Information Extensive-Form Games

As large language models (LLMs) become widely deployed, their outputs can be copied, transformed, and redistributed at scale without reliable evidence of origin, creating risks for trust, accountability, intellectual property (IP) protection, and high-stakes decision-making. LLM watermarking addresses this problem by embedding detectable signals into text during or after generation. However, existing methods vary in design assumptions, threat models, and evaluation criteria, while deployment choices such as watermark placement, detection authority, and key management affect reliability, security, and scalability. This paper systematizes LLM watermarking as provenance infrastructure for large-scale data ecosystems. We organize existing approaches along four deployment dimensions: insertion point, verification authority, operational state, and transformation threat model, and relate them to the big data requirements of Volume, Velocity, Variety, Veracity, and Value. We further introduce a Big Data Watermarking Readiness framework centered on four deployment workloads: online generation, streaming detection, transformation pipelines, and ecosystem governance. The framework connects these workloads to system-level requirements including throughput, false-positive control, robustness, cross-domain reliability, governance, and downstream utility. Our analysis highlights a gap between benchmark performance and deployment readiness: false positives accumulate at scale, repeated transformations weaken watermark signals, computational overhead can limit online deployment, and centralized verification can create governance bottlenecks. We conclude with an evaluation blueprint and research directions for scalable, trustworthy provenance in big data ecosystems.

We introduce Stateless Bernoulli Watermarking (SBW), a new statistical watermark for Large Language Models that determines green list membership through independent per-token Bernoulli trials. Unlike KGW's vocabulary permutation or SynthID's multi-layer tournament, SBW requires only a single comparison per token against a counter-based random number generator, reducing membership complexity to $O(1)$ and enabling single-kernel execution with zero intermediate allocations. We prove that this formulation preserves the same detection guarantees as fixed-size green lists: the z-score test remains $\mathcal{N}(0,1)$ under the null. The stateless architecture enables capabilities unavailable to existing methods: full-vocabulary self-salt watermarking (over 6000$\times$ faster than KGW's self-salt and 2$\times$ faster than SynthID despite biasing the entire vocabulary with candidate-dependent seeding) and architectural compatibility with distributed inference. In end-to-end generation benchmarks, SBW adds less than 1% overhead at all batch sizes. We additionally identify hash function design as a previously unexplored axis for watermark quality, showing that a GPU-native Jenkins hash improves null calibration by 1.8$\times$ while producing more diverse text. Experiments across two seeding schemes and eight $(γ, δ)$ configurations confirm statistical equivalence with ROC-AUC differences below 0.01.

Watermarking LLM-generated text is an important task for tracing its provenance. Existing LLM watermarks preserve provenance under editing, but this same robustness allows an adversary to alter critical content while retaining attribution, a vulnerability known as piggyback spoofing. We introduce an innovative watermark that jointly provides provenance and tamper evidence. It co-embeds a robust signal and a fragile signal into each generated token. The signals share the same mechanism but use independent keys and different seeding windows over normalized text, making one resilient to edits and the other sensitive to reader-visible changes. Multiple rounds of unbiased tournament reweighting preserve the expected generation distribution, while a periodic round-allocation pattern controls the trade-off between the two signals. At detection, their scores form a two-dimensional space supporting three decisions: Intact, Tampered, and No-Watermark. Across two large language models and two prompt datasets, our method demonstrates the highest tamper-detection rate among the evaluated methods while maintaining competitive attribution robustness and perplexity. Ablation studies show that reliable three-state detection requires a well-defined notion of intactness, co-embedding of the two signals, and complementary sensitivity to edits.