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Motivated by Cournot models, this paper proposes novel models of the noncooperative and cooperative differential games with density constraints in infinite dimensions, where markets consist of infinite firms and demand dynamics are governed…
We study learnability of mixed-strategy Nash Equilibrium (NE) in general finite games using higher-order replicator dynamics as well as classes of higher-order uncoupled heterogeneous dynamics. In higher-order uncoupled learning dynamics,…
In this paper, Nash equilibrium seeking among a network of players is considered. Different from many existing works on Nash equilibrium seeking in non-cooperative games, the players considered in this paper cannot directly observe the…
This paper delves into studying the differences and connections between open-loop and closed-loop strategies for the linear quadratic (LQ) mean field games (MFGs) by the direct approach. The investigation begins with the finite-population…
We study the robust Nash equilibrium (RNE) for a class of games in communications systems and networks where the impact of users on each other is an additive function of their strategies. Each user measures this impact, which may be…
While Nash equilibrium in extensive-form games is well understood, very little is known about the properties of extensive-form correlated equilibrium (EFCE), both from a behavioral and from a computational point of view. In this setting,…
In this note, we study a class of deterministic finite-horizon linear-quadratic difference games with coupled affine inequality constraints involving both state and control variables. We show that the necessary conditions for the existence…
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…
In finite games mixed Nash equilibria always exist, but pure equilibria may fail to exist. To assess the relevance of this nonexistence, we consider games where the payoffs are drawn at random. In particular, we focus on games where a large…
This paper resolves the open question of designing near-optimal algorithms for learning imperfect-information extensive-form games from bandit feedback. We present the first line of algorithms that require only…
We study finite-horizon two-player zero-sum differential games with one-sided payoff information ($G$), where the informed player (P1) knows the game payoff, while P2 only has a public belief over a finite set of possible payoffs. In this…
This paper considers convex games involving multiple agents that aim to minimize their own cost functions using locally available information. A common assumption in the study of such games is that the agents are symmetric, meaning that…
Examining the behavior of multi-agent systems is vitally important to many emerging distributed applications - game theory has emerged as a powerful tool set in which to do so. The main approach of game-theoretic techniques is to model…
Game theory has emerged as a powerful framework for modeling a large range of multi-agent scenarios. Many algorithmic solutions require discrete, finite games with payoffs that have a closed-form specification. In contrast, many real-world…
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…
Game-theoretic techniques and equilibria analysis facilitate the design and verification of competitive systems. While algorithmic complexity of equilibria computation has been extensively studied, practical implementation and application…
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…
Learning problems commonly exhibit an interesting feedback mechanism wherein the population data reacts to competing decision makers' actions. This paper formulates a new game theoretic framework for this phenomenon, called "multi-player…
This paper proposes a novel approach for local convergence to Nash equilibrium in quadratic noncooperative games based on a distributed Lie-bracket extremum seeking control scheme. This is the first instance of noncooperative games being…
The goal of agents in multi-agent environments is to maximize total reward against the opposing agents that are encountered. Following a game-theoretic solution concept, such as Nash equilibrium, may obtain a strong performance in some…