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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 consider a class of Nash games, termed as aggregative games, being played over a networked system. In an aggregative game, a player's objective is a function of the aggregate of all the players' decisions. Every player maintains an…
We discuss similarities and differences between systems of interacting players maximizing their individual payoffs and particles minimizing their interaction energy. Long-run behavior of stochastic dynamics of spatial games with multiple…
This paper studies relative arbitrage opportunities in a market with competitive investors through stochastic differential games in the limit as the number of players tends to infinity. With common noises introduced by the stock…
We study stationary mean field games with singular controls in which the representative player interacts with a long-time weighted average of the population through a discounted and an ergodic performance criterion. This class of games…
This paper studies singular mean field control problems and singular mean field stochastic differential games. Both sufficient and necessary conditions for the optimal controls and for the Nash equilibrium are obtained. Under some…
The use of game theoretic models has been quite successful in describing various cooperative and non-cooperative optimization problems in networks and other domains of computer systems. In this paper, we study an application of game…
We introduce a mean field model for optimal holding of a representative agent of her peers as a natural expected scaling limit from the corresponding $N-$agent model. The induced mean field dynamics appear naturally in a form which is not…
We discuss and compare two methods of investigations for the asymptotic regime of stochastic differential games with a finite number of players as the number of players tends to the infinity. These two methods differ in the order in which…
This article is related to risk-sensitive nonzero-sum stochastic differential games in the Markovian framework. This game takes into account the attitudes of the players toward risk and the utility is of exponential form. We show the…
Research in adversarial learning follows a cat and mouse game between attackers and defenders where attacks are proposed, they are mitigated by new defenses, and subsequently new attacks are proposed that break earlier defenses, and so on.…
A growing body of work in game theory extends the traditional Stackelberg game to settings with one leader and multiple followers who play a Nash equilibrium. Standard approaches for computing equilibria in these games reformulate the…
Focusing on stochastic systems arising in mean-field models, the systems under consideration belong to the class of switching diffusions, in which continuous dynamics and discrete events coexist and interact. The discrete events are modeled…
Evolutionary game theory is a framework to formalize the evolution of collectives ("populations") of competing agents that are playing a game and, after every round, update their strategies to maximize individual payoffs. There are two…
Motivated by the recent applications of game-theoretical learning techniques to the design of distributed control systems, we study a class of control problems that can be formulated as potential games with continuous action sets, and we…
We consider a multi-player stochastic differential game with linear McKean-Vlasov dynamics and quadratic cost functional depending on the variance and mean of the state and control actions of the players in open-loop form. Finite and…
We consider an $N$-player game where the states of the players evolve with time as Stochastic Differential Equations (SDEs) with interaction only in the drift terms. Each player controls the drift of the SDE satisfied by her state process,…
Mean field games are studied in the framework of controlled martingale problems, and general existence theorems are proven in which the equilibrium control is Markovian. The framework is flexible enough to include degenerate volatility,…
We study a dynamic game with a large population of players who choose actions from a finite set in continuous time. Each player has a state in a finite state space that evolves stochastically with their actions. A player's reward depends…
We study a class of graphon particle systems with time-varying random coefficients. In a graphon particle system, the interactions among particles are characterized by the coupled mean field terms through an underlying graphon and the…