Learning to accurately represent environmental uncertainty is crucial for adaptive and optimal behaviors in various cognitive tasks. However, it remains unclear how the human brain, constrained by finite cognitive resources, constructs an internal model from an infinite space of probability distributions. In this study, we explore how these learned distributions deviate from the ground truth, resulting in observable inconsistency in a novel structured density estimation task. During each trial, human participants were asked to form and report the latent probability distribution functions underlying sequentially presented independent observations. As the number of observations increased, the reported predictive density became closer to the ground truth. Nevertheless, we observed an intriguing inconsistency in human structure estimation, specifically a large error in the number of reported clusters.

With the practical implementation of connected and autonomous vehicles (CAVs), the traffic system is expected to remain a mix of CAVs and human-driven vehicles (HVs) for the foreseeable future. To enhance safety and traffic efficiency, the trajectory planning strategies of CAVs must account for the influence of HVs, necessitating accurate HV trajectory prediction. Current research often assumes that human drivers have perfect knowledge of all vehicles' objectives, an unrealistic premise. This paper bridges the gap by leveraging hypergame theory to account for cognitive and perception limitations in HVs. We model human bounded rationality without assuming them to be merely passive followers and propose a hierarchical cognition modeling framework that captures cognitive relationships among vehicles. We further analyze the cognitive stability of the system, proving that the strategy profile where all vehicles adopt cognitively equilibrium strategies constitutes a hyper Nash equilibrium when CAVs accurately learn HV parameters. To achieve this, we develop an inverse learning algorithm for distributed intention interpretation via vehicle-to-everything (V2X) communication, which extends the framework to both offline and online scenarios. Additionally, we introduce a distributed trajectory prediction and planning approach for CAVs, leveraging the learned parameters in real time. Simulations in highway lane-changing scenarios demonstrate the proposed method's accuracy in parameter learning, robustness to noisy trajectory observations, and safety in HV trajectory prediction. The results validate the effectiveness of our method in both offline and online implementations.

One primary objective of game theory is to predict the behaviors of agents through equilibrium concepts in a given game. In practice, however, we may observe some equilibrium behaviors of agents, but the game itself turns out to be unknown.

Power is a key concept in AI safety: power-seeking as an instrumental goal, sudden or gradual disempowerment of humans, power balance in human-AI interaction and international AI governance. At the same time, power as the ability to pursue diverse goals is essential for wellbeing. This paper explores the idea of promoting both safety and wellbeing by forcing AI agents explicitly to empower humans and to manage the power balance between humans and AI agents in a desirable way. Using a principled, partially axiomatic approach, we design a parametrizable and decomposable objective function that represents an inequality- and risk-averse long-term aggregate of human power. It takes into account humans' bounded rationality and social norms, and, crucially, considers a wide variety of possible human goals. We derive algorithms for computing that metric by backward induction or approximating it via a form of multi-agent reinforcement learning from a given world model. We exemplify the consequences of (softly) maximizing this metric in a variety of paradigmatic situations and describe what instrumental sub-goals it will likely imply. Our cautious assessment is that softly maximizing suitable aggregate metrics of human power might constitute a beneficial objective for agentic AI systems that is safer than direct utility-based objectives.

-- Enhancing simulation environments to replicate real-world driver behavior, i.e., more humanlike sim agents, is essential for developing autonomous vehicle technology. In the context of highway merging, previous works have studied the operational-level yielding dynamics of lag vehicles in response to a merging car at highway on-ramps. Other works focusing on tactical decision modeling generally consider limited action sets or utilize payoff functions with large parameter sets and limited payoff bounds. In this work, we aim to improve the simulation of the highway merge scenario by targeting a game theoretic model for tactical decision-making with improved payoff functions and lag actions. We couple this with an underlying dynamics model to have a unified decision and dynamics model that can capture merging interactions and simulate more realistic interactions in an explainable and interpretable fashion. The proposed model demonstrated good reproducibility of complex interactions when validated on a real-world dataset. The model was finally integrated into a high-fidelity simulation environment and confirmed to have adequate computation time efficiency for use in large-scale simulations to support autonomous vehicle development. Simulation-based evaluation has become an indispensable tool in the development and testing of Intelligent Transportation Systems (ITS), offering a safe and controllable environment for replicating complex real-world interactions.

We introduce the LLM-Nash framework, a game-theoretic model where agents select reasoning prompts to guide decision-making via Large Language Models (LLMs). Unlike classical games that assume utility-maximizing agents with full rationality, this framework captures bounded rationality by modeling the reasoning process explicitly. Equilibrium is defined over the prompt space, with actions emerging as the behavioral output of LLM inference. This approach enables the study of cognitive constraints, mindset expressiveness, and epistemic learning. Through illustrative examples, we show how reasoning equilibria can diverge from classical Nash outcomes, offering a new foundation for strategic interaction in LLM-enabled systems.

Game-Theoretic Modeling of V ehicle Unprotected Left Turns Considering Drivers' Bounded Rationality Abstract --Modeling the decision-making behavior of vehicles presents unique challenges, particularly during unprotected left turns at intersections, where the uncertainty of human drivers is especially pronounced. In this context, connected autonomous vehicle (CA V) technology emerges as a promising avenue for effectively managing such interactions while ensuring safety and efficiency. Traditional approaches, often grounded in game theory assumptions of perfect rationality, may inadequately capture the complexities of real-world scenarios and drivers' decision-making errors. T o fill this gap, we propose a novel decision-making model for vehicle unprotected left-turn scenarios, integrating game theory with considerations for drivers' bounded rationality. Our model, formulated as a two-player normal-form game solved by a quantal response equilibrium (QRE), offers a more nuanced depiction of driver decision-making processes compared to Nash equilibrium (NE) models. Leveraging an Expectation-Maximization (EM) algorithm coupled with a subtle neural network trained on precise microscopic vehicle trajectory data, we optimize model parameters to accurately reflect drivers' interaction-aware bounded rationality and driving styles. Through comprehensive simulation experiments, we demonstrate the efficacy of our proposed model in capturing the interaction-aware bounded rationality and decision tendencies between players. The proposed model proves to be more realistic and efficient than NE models in unprotected left-turn scenarios. Our findings contribute valuable insights into the vehicle decision-making behaviors with bounded rationality, thereby informing the development of more robust and realistic autonomous driving systems. Connected autonomous vehicle (CA V) refers to a vehicle that can operate autonomously and communicate with other vehicles and infrastructure to enhance safety and efficiency. This work was supported by grants from National Key Research and Development Program of China (2022YFB2503200), Tsinghua University-Mercedes Benz Joint Institute for Sustainable Mobility. Consequently, there arises an urgent need to develop models that enable the operation of CA Vs within mixed traffic environments, enabling them to anticipate the intentions of surrounding human drivers and make human-like decisions based on these expectations and feedback. In the context of mixed traffic environments, one of the most prevalent scenarios entails vehicles executing unprotected left turns at signalized intersections.

Modelling bounded rational decision-making through information constrained processing provides a principled approach for representing departures from rationality within a reinforcement learning framework, while still treating decision-making as an optimization process. However, existing approaches are generally based on Entropy, Kullback-Leibler divergence, or Mutual Information. In this work, we highlight issues with these approaches when dealing with ordinal action spaces. Specifically, entropy assumes uniform prior beliefs, missing the impact of a priori biases on decision-makings. KL-Divergence addresses this, however, has no notion of "nearness" of actions, and additionally, has several well known potentially undesirable properties such as the lack of symmetry, and furthermore, requires the distributions to have the same support (e.g. positive probability for all actions). Mutual information is often difficult to estimate. Here, we propose an alternative approach for modeling bounded rational RL agents utilising Wasserstein distances. This approach overcomes the aforementioned issues. Crucially, this approach accounts for the nearness of ordinal actions, modeling "stickiness" in agent decisions and unlikeliness of rapidly switching to far away actions, while also supporting low probability actions, zero-support prior distributions, and is simple to calculate directly.