# Predicting Human Behavior in Unrepeated, Simultaneous-Move Games

arXiv: https://arxiv.org/abs/1306.0918 · HTML: https://mlsanity.com/paper/1306.0918/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jun 2013.

## Built on by (most cited first, 10 of 10)

- [Capturing the Complexity of Human Strategic Decision-Making with Machine Learning](https://mlsanity.com/paper/2408.07865/) (2024)
- [Simplex Neural Population Learning: Any-Mixture Bayes-Optimality in Symmetric Zero-sum Games](https://mlsanity.com/paper/2205.15879/) (2022)
- [Learning Human Rewards by Inferring Their Latent Intelligence Levels in Multi-Agent Games: A Theory-of-Mind Approach with Application to Driving Data](https://mlsanity.com/paper/2103.04289/) (2021)
- [A Mental-Model Centric Landscape of Human-AI Symbiosis](https://mlsanity.com/paper/2202.09447/) (2022)
- [Risk-Sensitive Multi-Agent Reinforcement Learning in Network Aggregative Markov Games](https://mlsanity.com/paper/2402.05906/) (2024)
- [CHBench: A Cognitive Hierarchy Benchmark for Evaluating Strategic Reasoning Capability of LLMs](https://mlsanity.com/paper/2508.11944/) (2025)
- [How to Evaluate Behavioral Models](https://mlsanity.com/paper/2306.04778/) (2023)
- [Risk Sensitivity in Markov Games and Multi-Agent Reinforcement Learning: A Systematic Review](https://mlsanity.com/paper/2406.06041/) (2024)
- [ElementaryNet: A Non-Strategic Neural Network for Predicting Human Behavior in Normal-Form Games](https://mlsanity.com/paper/2503.05925/) (2025)
- [The Internal Anatomy of Strategic Choice in Large Language Models](https://mlsanity.com/paper/2609.07478/) (2026)

## Abstract (arXiv)

It is common to assume that agents will adopt Nash equilibrium strategies; however, experimental studies have demonstrated that Nash equilibrium is often a poor description of human players' behavior in unrepeated normal-form games. In this paper, we analyze five widely studied models (Quantal Response Equilibrium, Level-k, Cognitive Hierarchy, QLk, and Noisy Introspection) that aim to describe actual, rather than idealized, human behavior in such games. We performed what we believe is the most comprehensive meta-analysis of these models, leveraging ten different data sets from the literature recording human play of two-player games. We began by evaluating the models' generalization or predictive performance, asking how well a model fits unseen test data after having had its parameters calibrated based on separate training data. Surprisingly, we found that what we dub the QLk model of Stahl & Wilson (1994) consistently achieved the best performance. Motivated by this finding, we describe methods for analyzing the posterior distributions over a model's parameters. We found that QLk's parameters were being set to values that were not consistent with their intended economic interpretations. We thus explored variations of QLk, ultimately identifying a new model family that has fewer parameters, gives rise to more parsimonious parameter values, and achieves better predictive performance.