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ElementaryNet: A Non-Strategic Neural Network for Predicting Human Behavior in Normal-Form Games

Greg d'Eon, Hala Murad, Kevin Leyton-Brown, James R. Wright

TL;DR

This work addresses predicting human behavior in unrepeated normal-form games and the interpretability of predictive models. It shows that GameNet’s level-0 can emulate strategic reasoning (e.g., $q_1(G)=QBR_1(\text{maxmax}_2(G); 1, G)$) and introduces ElementaryNet, a non-strategic neural network built from potential functions that acts as a bottleneck to prevent strategic inference. Empirically, ElementaryNet paired with a QCHp strategic model achieves predictive performance indistinguishable from the best GameNet while enabling interpretable analysis of iterative reasoning and level-0 sophistication. The results highlight the value of explicit non-strategic bottlenecks for interpretability and point to promising directions for extending these ideas to more complex strategic settings.

Abstract

Behavioral game theory models serve two purposes: yielding insights into how human decision-making works, and predicting how people would behave in novel strategic settings. A system called GameNet represents the state of the art for predicting human behavior in the setting of unrepeated simultaneous-move games, combining a simple "level-k" model of strategic reasoning with a complex neural network model of non-strategic "level-0" behavior. Although this reliance on well-established ideas from cognitive science ought to make GameNet interpretable, the flexibility of its level-0 model raises the possibility that it is able to emulate strategic reasoning. In this work, we prove that GameNet's level-0 model is indeed too general. We then introduce ElementaryNet, a novel neural network that is provably incapable of expressing strategic behavior. We show that these additional restrictions are empirically harmless, with ElementaryNet and GameNet having statistically indistinguishable performance. We then show how it is possible to derive insights about human behavior by varying ElementaryNet's features and interpreting its parameters, finding evidence of iterative reasoning, learning about the depth of this reasoning process, and showing the value of a rich level-0 specification.

ElementaryNet: A Non-Strategic Neural Network for Predicting Human Behavior in Normal-Form Games

TL;DR

This work addresses predicting human behavior in unrepeated normal-form games and the interpretability of predictive models. It shows that GameNet’s level-0 can emulate strategic reasoning (e.g., ) and introduces ElementaryNet, a non-strategic neural network built from potential functions that acts as a bottleneck to prevent strategic inference. Empirically, ElementaryNet paired with a QCHp strategic model achieves predictive performance indistinguishable from the best GameNet while enabling interpretable analysis of iterative reasoning and level-0 sophistication. The results highlight the value of explicit non-strategic bottlenecks for interpretability and point to promising directions for extending these ideas to more complex strategic settings.

Abstract

Behavioral game theory models serve two purposes: yielding insights into how human decision-making works, and predicting how people would behave in novel strategic settings. A system called GameNet represents the state of the art for predicting human behavior in the setting of unrepeated simultaneous-move games, combining a simple "level-k" model of strategic reasoning with a complex neural network model of non-strategic "level-0" behavior. Although this reliance on well-established ideas from cognitive science ought to make GameNet interpretable, the flexibility of its level-0 model raises the possibility that it is able to emulate strategic reasoning. In this work, we prove that GameNet's level-0 model is indeed too general. We then introduce ElementaryNet, a novel neural network that is provably incapable of expressing strategic behavior. We show that these additional restrictions are empirically harmless, with ElementaryNet and GameNet having statistically indistinguishable performance. We then show how it is possible to derive insights about human behavior by varying ElementaryNet's features and interpreting its parameters, finding evidence of iterative reasoning, learning about the depth of this reasoning process, and showing the value of a rich level-0 specification.

Paper Structure

This paper contains 39 sections, 8 theorems, 17 equations, 11 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Existing Behavioral Models
  4. GameNet
  5. Non-Strategic Behavioral Models
  6. GameNet's Feature Layers are Strategic
  7. A Non-Strategic Neural Network
  8. ElementaryNet
  9. ElementaryNet is Non-Strategic
  10. Experiments
  11. Experimental Setup
  12. Data.
  13. Training.
  14. Confidence intervals.
  15. Comparing to GameNet
  16. ...and 24 more sections

Key Result

theorem 1

WLBnonstrategic Let $g_i^1, \dots, g_i^K$ be elementary behavioral models, and let $w_1, \dots, w_K$ be non-negative weights summing to 1. Then, the convex combination $f_i(G) = \sum_{k=1}^K w_k g_i^k(G)$ is a weakly non-strategic behavioral model.

Figures (11)

  • Figure 1: GameNet's feature layers.
  • Figure 2: The ElementaryNet architecture. (a) The full model; (b) a potential function; and (c) a response function.
  • Figure 3: ElementaryNet and GameNet level-0 models trained with a QCH-Poisson strategic model. The best ElementaryNet models are similar in performance to the best GameNet model. Lower values are better.
  • Figure 4: ElementaryNet models with no QCH model. Purely non-strategic models fit the data extremely poorly.
  • Figure 5:
  • ...and 6 more figures

Theorems & Definitions (23)

  • definition 1
  • definition 2
  • definition 3
  • definition 4
  • definition 5
  • definition 6
  • definition 7
  • theorem 1
  • theorem 2
  • proof
  • ...and 13 more