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This paper proposes to use probabilistic model checking to synthesize optimal robot policies in multi-tasking autonomous systems that are subject to human-robot interaction. Given the convincing empirical evidence that human behavior can be…
This paper presents a game theoretic formulation of a graph traversal problem, with applications to robots moving through hazardous environments in the presence of an adversary, as in military and security scenarios. The blue team of robots…
In this tutorial, we provide an introduction to machine learning methods for finding Nash equilibria in games with large number of agents. These types of problems are important for the operations research community because of their…
The noncooperative Nash equilibrium solution of classical games corresponds to a rational expectations attitude on the part of the players. However, in many cases, games played by human players have outcomes very different from Nash…
A growing line of work reframes preference-based fine-tuning of large language models game-theoretically: Nash Learning from Human Feedback (NLHF) recasts the problem as a zero-sum game over policies. However, optimization is over expected…
This paper considers data-based solutions of linear-quadratic nonzero-sum differential games. Two cases are considered. First, the deterministic game is solved and Nash equilibrium strategies are obtained by using persistently excited data…
Many efficient algorithms have been designed to recover Nash equilibria of various classes of finite games. Special classes of continuous games with infinite strategy spaces, such as polynomial games, can be solved by semidefinite…
Nash equilibria provide a principled framework for modeling interactions in multi-agent decision-making and control. However, many equilibrium-seeking methods implicitly assume that each agent has access to the other agents' objectives and…
Zero-sum Linear Quadratic (LQ) games are fundamental in optimal control and can be used (i)~as a dynamic game formulation for risk-sensitive or robust control and (ii)~as a benchmark setting for multi-agent reinforcement learning with two…
In security games, the solution concept commonly used is that of a Stackelberg equilibrium where the defender gets to commit to a mixed strategy. The motivation for this is that the attacker can repeatedly observe the defender's actions and…
Nash equilibrium is one of the most influential solution concepts in game theory. With the development of computer science and artificial intelligence, there is an increasing demand on Nash equilibrium computation, especially for Internet…
In mobile robotics and autonomous driving, it is natural to model agent interactions as the Nash equilibrium of a noncooperative, dynamic game. These methods inherently rely on observations from sensors such as lidars and cameras to…
Dynamic nonzero sum games are widely used to model multi agent decision making in control, economics, and related fields. Classical methods for computing Nash equilibria, especially in linear quadratic settings, rely on strong structural…
Game theory is playing more and more important roles in understanding complex systems and in investigating intelligent machines with various uncertainties. As a starting point, we consider the classical two-player zero-sum linear-quadratic…
This paper presents a novel data-driven approach for approximating the $\varepsilon$-Nash equilibrium in continuous-time linear quadratic Gaussian (LQG) games, where multiple agents interact with each other through their dynamics and…
The game in which acts of participants don't have an adequate description in terms of Boolean logic and classical theory of probabilities is considered. The model of the game interaction is constructed on the basis of a non-distributive…
Computational aspects of solution notions such as Nash equilibrium have been extensively studied, including settings where the ultimate goal is to find an equilibrium that possesses some additional properties. Furthermore, in order to…
The paper is concerned with a zero-sum Stackelberg stochastic linear-quadratic (LQ, for short) differential game over finite horizons. Under a fairly weak condition, the Stackelberg equilibrium is explicitly obtained by first solving a…
This paper aims to reduce the communication and computation costs of the Nash equilibrium seeking strategy for the $N$-coalition noncooperative games proposed in [1]. The objective is achieved in two manners: 1. An interference graph is…
Even when confronted with the same data, agents often disagree on a model of the real-world. Here, we address the question of how interacting heterogenous agents, who disagree on what model the real-world follows, optimize their trading…