Related papers: Nested Extremum Seeking Converges to Stackelberg E…
The concept of leader--follower (or Stackelberg) equilibrium plays a central role in a number of real--world applications of game theory. While the case with a single follower has been thoroughly investigated, results with multiple…
We study the problem of calculating transport properties of interacting quantum systems, specifically electrical and thermal conductivities, by computing the non-equilibrium steady state (NESS) of the system biased by contacts. Our approach…
Network congestion games are a convenient model for reasoning about routing problems in a network: agents have to move from a source to a target vertex while avoiding congestion, measured as a cost depending on the number of players using…
AI in Math deals with mathematics in a constructive manner so that reasoning becomes automated, less laborious, and less error-prone. For algorithms, the question becomes how to automate analyses for specific problems. For the first time,…
We propose projection-free sequential algorithms for linear-quadratic dynamics games. These policy gradient based algorithms are akin to Stackelberg leadership model and can be extended to model-free settings. We show that if the leader…
In multi-agent autonomous systems, deception is a fundamental concept which characterizes the exploitation of unbalanced information to mislead victims into choosing oblivious actions. This effectively alters the system's long term…
Extremum Seeking (ES) is an effective real-time optimization method for PDE systems in cascade with nonlinear quadratic maps. To address PDEs in the feedback loop, a boundary control law and a re-design of the additive probing signal are…
We address Nash equilibrium problems in a partial-decision information scenario, where each agent can only exchange information with some neighbors, while its cost function possibly depends on the strategies of all agents. We characterize…
We explore the power of semidefinite programming (SDP) for finding additive $epsilon$-approximate Nash equilibria in bimatrix games. We introduce an SDP relaxation for a quadratic programming formulation of the Nash equilibrium (NE) problem…
We consider a variant of the hide-and-seek game in which a seeker inspects multiple hiding locations to find multiple items hidden by a hider. Each hiding location has a maximum hiding capacity and a probability of detecting its hidden…
The concept of Nash equilibrium (NE), pivotal within game theory, has garnered widespread attention across numerous industries. Recent advancements introduced several quantum Nash solvers aimed at identifying pure strategy NE solutions…
In this work, we provide a structural characterization of the possible Nash equilibria in the well-studied class of security games with additive utility. Our analysis yields a classification of possible equilibria into seven types and we…
This paper considers a class of noncooperative games in which the feasible decision sets of all players are coupled together by a coupled inequality constraint. Adopting the variational inequality formulation of the game, we first introduce…
We study the sample complexity of identifying the pure strategy Nash equilibrium (PSNE) in a two-player zero-sum matrix game with noise. Formally, we are given a stochastic model where any learner can sample an entry $(i,j)$ of the input…
In the theory of multi-agent systems, deception refers to the strategic manipulation of information to influence the behavior of other agents, ultimately altering the long-term dynamics of the entire system. Recently, this concept has been…
The framework of multi-agent learning explores the dynamics of how individual agent strategies evolve in response to the evolving strategies of other agents. Of particular interest is whether or not agent strategies converge to well known…
The Nash Equilibrium (NE) assumes rational play in imperfect-information Extensive-Form Games (EFGs) but fails to ensure optimal strategies for off-equilibrium branches of the game tree, potentially leading to suboptimal outcomes in…
One key in real-life Nash equilibrium applications is to calibrate players' cost functions. To leverage the approximation ability of neural networks, we proposed a general framework for optimizing and learning Nash equilibrium using neural…
The design of small scale non-equilibrium steady states (NESS) is a challenging, open ended question. While similar equilibrium problems are tractable using standard thermodynamics, a generalized description for non-equilibrium systems is…
We propose two algorithms that can find local minima faster than the state-of-the-art algorithms in both finite-sum and general stochastic nonconvex optimization. At the core of the proposed algorithms is $\text{One-epoch-SNVRG}^+$ using…