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Quantifying Feature Importance of Games and Strategies via Shapley Values

Satoru Fujii

TL;DR

The paper addresses the explainability gap in game AI by introducing two Shapley-based metrics: Shapley Game Feature Importance (SGFI) for global game-level interpretation and Shapley Strategy Feature Importance (SSFI) for local strategy explanations. SGFI quantifies how obscuring subsets of game features affects the target player's expected return, while SSFI decomposes a given AI's strategy into per-feature contributions via permutation-based attribution. The authors ground the methods in extensive-form game theory, exploitability, and abstraction, and validate them empirically on the Goofspiel benchmark, showing that features like Center and Deck are typically more influential and that SSFI decompositions align with intuitive strategic reasoning. Overall, these explainability tools aim to enhance human understanding and collaboration with AI in complex strategic settings, while providing principled, algorithmic insights into feature importance.

Abstract

Recent advances in game informatics have enabled us to find strong strategies across a diverse range of games. However, these strategies are usually difficult for humans to interpret. On the other hand, research in Explainable Artificial Intelligence (XAI) has seen a notable surge in scholarly activity. Interpreting strong or near-optimal strategies or the game itself can provide valuable insights. In this paper, we propose two methods to quantify the feature importance using Shapley values: one for the game itself and another for individual AIs. We empirically show that our proposed methods yield intuitive explanations that resonate with and augment human understanding.

Quantifying Feature Importance of Games and Strategies via Shapley Values

TL;DR

The paper addresses the explainability gap in game AI by introducing two Shapley-based metrics: Shapley Game Feature Importance (SGFI) for global game-level interpretation and Shapley Strategy Feature Importance (SSFI) for local strategy explanations. SGFI quantifies how obscuring subsets of game features affects the target player's expected return, while SSFI decomposes a given AI's strategy into per-feature contributions via permutation-based attribution. The authors ground the methods in extensive-form game theory, exploitability, and abstraction, and validate them empirically on the Goofspiel benchmark, showing that features like Center and Deck are typically more influential and that SSFI decompositions align with intuitive strategic reasoning. Overall, these explainability tools aim to enhance human understanding and collaboration with AI in complex strategic settings, while providing principled, algorithmic insights into feature importance.

Abstract

Recent advances in game informatics have enabled us to find strong strategies across a diverse range of games. However, these strategies are usually difficult for humans to interpret. On the other hand, research in Explainable Artificial Intelligence (XAI) has seen a notable surge in scholarly activity. Interpreting strong or near-optimal strategies or the game itself can provide valuable insights. In this paper, we propose two methods to quantify the feature importance using Shapley values: one for the game itself and another for individual AIs. We empirically show that our proposed methods yield intuitive explanations that resonate with and augment human understanding.
Paper Structure (16 sections, 1 theorem, 8 equations, 7 figures)

This paper contains 16 sections, 1 theorem, 8 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Notation and Background
  3. Extensive-form Games
  4. Exploitability
  5. Counterfactual Regret Minimization (CFR)
  6. Abstraction
  7. Feature Importance and Shapley Value
  8. Related Work
  9. Descriptions of Our Methods
  10. Shapley Game Feature Importance
  11. Shapley Strategy Feature Importance
  12. Experiments
  13. Goofspiel
  14. SGFI of Goofspiel
  15. SSFI of Goofspiel AI
  16. ...and 1 more sections

Key Result

theorem 1

If abstraction $\alpha'_i$ is a subpartion of $\alpha_i$,

Figures (7)

  • Figure 1: SGFI of Goofspiel
  • Figure 2: Expected return convergence of the target player for different abstractions. Legends denote elements in $S$.
  • Figure 3: Convergence of $u_i(\hat{\sigma}_i^{*, \alpha_i(\{j\})})$ and $u_i(\hat{\sigma}_i^{*, \alpha_i(\mathcal{M}-\{j\})})$. Legends denote elements in $S$.
  • Figure 4: Situation in $I^1$
  • Figure 5: SSFI of $\hat{\sigma}^*_1(I^1)$.
  • ...and 2 more figures

Theorems & Definitions (1)

  • theorem 1