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We study deterministic optimal control problems for differential games with finite horizon. We propose new approximations of the strategies in feedback form, and show error estimates and a convergence result of the value in some weak sense…
We study convergence rates of random-order best-response dynamics in games on networks with linear best responses and strategic substitutes. Combining formal analysis with numerical simulations we identify phenomena that lead to slow…
In this paper, we consider a Nash equilibrium seeking problem for a class of high-order multi-agent systems with unknown dynamics. Different from existing results for single integrators, we aim to steer the outputs of this class of…
We introduce Game networks (G nets), a novel representation for multi-agent decision problems. Compared to other game-theoretic representations, such as strategic or extensive forms, G nets are more structured and more compact; more…
In this paper, we investigate the noncooperative games of multi-agent systems. Different from existing noncooperative games, our formulation involves the high-order nonlinear dynamics of players, and the communication topologies among…
Consider a set of agents who play a network game repeatedly. Agents may not know the network. They may even be unaware that they are interacting with other agents in a network. Possibly, they just understand that their payoffs depend on an…
Algorithmic game theory (AGT) focuses on the design and analysis of algorithms for interacting agents, with interactions rigorously formalized within the framework of games. Results from AGT find applications in domains such as online…
This paper fully studies distributed optimal consensus problem in non-directed dynamical networks. We consider a group of networked agents that are supposed to rendezvous at the optimal point of a collective convex objective function. Each…
In this paper, a time-varying distributed convex optimization problem is studied for continuous-time multi-agent systems. Control algorithms are designed for the cases of single-integrator and double-integrator dynamics. Two discontinuous…
We address the generalized Nash equilibrium seeking problem for a population of agents playing aggregative games with affine coupling constraints. We focus on semi-decentralized communication architectures, where there is a central…
We present two variants of a multi-agent reinforcement learning algorithm based on evolutionary game theoretic considerations. The intentional simplicity of one variant enables us to prove results on its relationship to a system of ordinary…
We consider the framework of average aggregative games, where the cost function of each agent depends on his own strategy and on the average population strategy. We focus on the case in which the agents are coupled not only via their cost…
In this paper, we study the consensus problem for continuous-time and discrete-time multi-agent systems in state-dependent switching networks. In each case, we first consider the networks with fixed connectivity, in which the communication…
Control of multi-agent systems via game theory is investigated. Assume a system level object is given, the utility functions for individual agents are designed to convert a multi-agent system into a potential game. First, for fixed…
Stochastic games have become a prevalent framework for studying long-term multi-agent interactions, especially in the context of multi-agent reinforcement learning. In this work, we comprehensively investigate the concept of constant-memory…
We study asynchronous dynamics in a network of interacting agents updating their binary states according to a time-varying threshold rule. Specifically, agents revise their state asynchronously by comparing the weighted average of the…
Considering a class of gradient-based multi-agent learning algorithms in non-cooperative settings, we provide local convergence guarantees to a neighborhood of a stable local Nash equilibrium. In particular, we consider continuous games…
Economic ensembles can be modeled as networks of interacting agents whose be-haviors are described in terms of game theory. The evolutionary paradigm has been applied to two-person games to discover strategies in this context.…
The problem of consensus in the presence of adversarially behaving agents has been studied extensively in the literature. The proposed algorithms typically guarantee that the consensus value lies within the convex hull of initial normal…
Multi-agent reinforcement learning methods have shown remarkable potential in solving complex multi-agent problems but mostly lack theoretical guarantees. Recently, mean field control and mean field games have been established as a…