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Stochastic dynamic teams and games are rich models for decentralized systems and challenging testing grounds for multi-agent learning. Previous work that guaranteed team optimality assumed stateless dynamics, or an explicit coordination…
We study the convergence properties of decentralized fictitious play (DFP) for the class of near-potential games where the incentives of agents are nearly aligned with a potential function. In DFP, agents share information only with their…
We study discrete-time mean-field Markov games with infinite numbers of agents where each agent aims to minimize its ergodic cost. We consider the setting where the agents have identical linear state transitions and quadratic cost…
Solving feedback Stackelberg games with nonlinear dynamics and coupled constraints, a common scenario in practice, presents significant challenges. This work introduces an efficient method for computing approximate local feedback…
Differential Dynamic Programming (DDP) is a popular technique used to generate motion for dynamic-legged robots in the recent past. However, in most cases, only the first-order partial derivatives of the underlying dynamics are used,…
Differential Dynamic Programming (DDP) is an efficient trajectory optimization algorithm relying on second-order approximations of a system's dynamics and cost function, and has recently been applied to optimize systems with time-invariant…
Starting from a heuristic learning scheme for N-person games, we derive a new class of continuous-time learning dynamics consisting of a replicator-like drift adjusted by a penalty term that renders the boundary of the game's strategy space…
We initiate the study of game dynamics in the population protocol model: $n$ agents each maintain a current local strategy and interact in pairs uniformly at random. Upon each interaction, the agents play a two-person game and receive a…
We address the generalized Nash equilibrium seeking problem in a partial-decision information scenario, where each agent can only exchange information with some neighbors, although its cost function possibly depends on the strategies of all…
In this paper, we consider the problem of finding a Nash equilibrium in a multi-player game over generally connected networks. This model differs from a conventional setting in that players have partial information on the actions of their…
This paper investigates the equilibrium convergence properties of a proposed algorithm for potential games with continuous strategy spaces in the presence of feedback delays, a main challenge in multi-agent systems that compromises the…
This paper introduces a differential dynamic programming (DDP) based framework for polynomial trajectory generation for differentially flat systems. In particular, instead of using a linear equation with increasing size to represent…
We study the class of reach-avoid dynamic games in which multiple agents interact noncooperatively, and each wishes to satisfy a distinct target criterion while avoiding a failure criterion. Reach-avoid games are commonly used to express…
A systematic framework for analyzing dynamical attributes of games has not been well-studied except for the special class of potential or near-potential games. In particular, the existing results have shortcomings in determining the…
We consider a dynamic programming (DP) approach to approximately solving an infinite-horizon constrained Markov decision process (CMDP) problem with a fixed initial-state for the expected total discounted-reward criterion with a…
Repeated games consider a situation where multiple agents are motivated by their independent rewards throughout learning. In general, the dynamics of their learning become complex. Especially when their rewards compete with each other like…
In this paper, we investigate the seeking of Nash equilibrium (NE) in a non-cooperative quadratic game where all agents exchange their delayed strategy information with their neighbors. To extend best-response algorithms to the delayed…
We introduce a new algorithm for the numerical computation of Nash equilibria of competitive two-player games. Our method is a natural generalization of gradient descent to the two-player setting where the update is given by the Nash…
We leverage best response dynamics to solve monotone variational inequalities on compact and convex sets. Specialization of the method to variational inequalities in game theory recovers convergence results to Nash equilibria when agents…
Game theory offers an interpretable mathematical framework for modeling multi-agent interactions. However, its applicability in real-world robotics applications is hindered by several challenges, such as unknown agents' preferences and…