Domain-Independent Game Abstraction using Word Embedding Techniques

Abstract: Many games of interest in the real world are often intractably large, thereby necessitating the use of game abstraction to shrink them in size, typically by many magnitudes. Over the last two decades, there have been significant advances in game abstraction; however, the domain-specific nature (usually poker) of much of the prior work prevents those techniques from being easily generalized to other settings without extensively analyzing the game at hand. In this paper, we propose a domain-independent approach to game abstraction, which applies word embedding techniques from the field of natural language processing. Treating each action as a word and gameplay data as a corpus, word vectors can be trained to represent each action as a real-valued vector, which can then be clustered to facilitate game abstraction. We also explore the use of foundational embedding models and show that action embeddings obtained this way can capture a surprising amount of information about the underlying game. Experimental results demonstrate that our proposed game abstraction technique is effective, although it does not outperform specialized algorithms tailored to specific games.

• The paper presents a novel approach that uses word embedding techniques to create scalable, domain-independent game abstractions.
• It employs NLP methods like GloVe and foundational embedding models to cluster game actions and validate strategic similarity via nearest neighbor analysis.
• The approach reduces exploitability in games like Kuhn Poker and Leduc Hold'em, though it trades off some optimality compared to domain-specific techniques.

Domain-Independent Game Abstraction via Word Embedding Techniques

Introduction and Motivation

The paper "Domain-Independent Game Abstraction using Word Embedding Techniques" (2605.15543) addresses the scalability challenge in solving large imperfect-information games by proposing a domain-independent game abstraction approach grounded in word embedding techniques from NLP. The core objective is to construct game abstractions—drastically reducing game size while retaining strategic features—without reliance on specialized, domain-specific metrics or expertise. This is in contrast to predominant abstraction literature, which is highly tailored to games such as poker and involves constructing abstractions via hand strength, equity metrics, or signal trees, often requiring infeasible tree enumeration for equivalence testing beyond poker.

Methodology

Action Embeddings via Word Embedding

The proposed method conceptualizes each game action as a word and sequences of actions from gameplay as analogous to a textual corpus. Action representations (embeddings) are constructed using established word embedding techniques such as:

• GloVe: Trained on large gameplay corpora, producing dense, fixed-dimensional vector representations for each action.
• Foundational Embedding Models: Off-the-shelf models such as OpenAI's text-embedding-3-small and Google's Gemini, which require human-readable textual encodings of actions to produce zero-shot action embeddings.

Actions are clustered in embedding space via $k$-means to produce the abstraction; strategically similar actions—those whose subtrees are structurally and payoff-isomorphic—tend to be co-located in the embedding space and thus grouped in the abstraction.

Empirical Justification

Observational studies are conducted to validate the premise that action embeddings capture latent game semantics. Nearest neighbor analysis in embedding space for chess and poker actions reveals strong alignment: moves with similar strategic properties (e.g., promotions, checks, pair hands in poker) cluster together, despite the models being entirely unaware of syntactic elements in the move notation. Notably, with GloVe trained solely on action tokens, the emergent structure in embedding space mirrors the structure exploited by hand-crafted poker abstractions.

Evaluation

Games and Metrics

Experiments are performed on:

• 256-Kuhn Poker: Simplified variant of Kuhn poker with 256-card deck.
• 13-Leduc Hold'em: Expansion of Leduc with 13 card ranks.

The main evaluation metric is exploitability of a Nash equilibrium lifted from the abstraction and played in the original (unabstracted) game. Secondary is the abstraction size, measured in the number of action sequences and utility matrix non-zeros.

Baselines

• Hand-Bucketing Baseline: Buckets hands by strength, leveraging domain knowledge; the standard in poker abstractions.
• Random Baseline: Actions are clustered at random.

Results

The proposed domain-independent abstraction outperforms the random baseline across multiple granularities of abstraction, regardless of whether action embeddings are generated via GloVe or foundational embedding models. As the abstraction becomes finer-grained, exploitability generally decreases. However, domain-specific hand-bucketing consistently yields lower exploitability for a given abstraction size. The approach does not surpass such specialized techniques in optimality, supporting the claim that there is a quality-versus-generality tradeoff.

An observed limitation is reliance on sufficient gameplay data for effective vector training, or—when using foundational embeddings—the necessity for sensible textual descriptions of actions, a nontrivial problem for some domains.

Practical and Theoretical Implications

The key implication is that effective, scalable abstraction can be achieved for arbitrary extensive-form games without exhaustive domain analysis, specialized metrics, or hand-crafted features. This has immediate practical value for rapid prototyping of AIs in novel games for which domain knowledge is limited or abstraction expertise is lacking.

Theoretically, it supports the hypothesis that general semantic features relevant to strategy can be captured through distributional statistics over gameplay, mirroring how semantics emerge in natural language. The approach unifies game abstraction with advances in representation learning, suggesting fruitful cross-pollination moving forward, e.g., by leveraging advances in contrastive training or context-sensitive representation as these evolve in NLP.

Additionally, the framework offers prospects for modeling human decision-making in games (e.g., via quantal-response equilibria) by fitting embeddings on human gameplay, enabling the study of implicit abstraction processes in human cognition.

Limitations and Future Directions

The approach’s abstraction quality, though superior to random clustering, is consistently surpassed by domain-tuned techniques. Moreover, when foundational embedding models are used, some degree of domain awareness is required for textual encoding, partially undermining the claim of total domain-independence.

Future research directions include:

• Integrating richer sequential context (e.g., via transformer-based sequence models).
• Exploring reinforcement learning-driven abstraction where vector representations are learned end-to-end with a solution algorithm.
• Adapting these techniques to more complex or continuous action spaces.
• Applying the abstraction methodology to real-world domains beyond recreational games, such as security games, auctions, or negotiation.
• Investigating application to information retrieval systems at the intersection of IR and games.

Conclusion

This work demonstrates that semantic representations from NLP, when repurposed for game actions, enable the construction of domain-independent game abstractions that are effective across diverse games without domain-specific engineering. While not outperforming bespoke methods that exploit game structure, the technique offers a scalable, practical abstraction tool well-suited as a strong baseline and avenue for further research in generalized AI game solving and human behavior modeling in strategic settings (2605.15543).