Related papers: Stochastic Adaptive Linear Quadratic Differential …
In this paper, we propose a numerical methodology for finding the closed-loop Nash equilibrium of stochastic delay differential games through deep learning. These games are prevalent in finance and economics where multi-agent interaction…
In this paper, we consider a linear quadratic stochastic two-person nonzero-sum differential game. Open-loop and closed-loop Nash equilibria are introduced. The existence of the former is characterized by the solvability of a system of…
In this paper, we consider two-player zero-sum matrix and stochastic games and develop learning dynamics that are payoff-based, convergent, rational, and symmetric between the two players. Specifically, the learning dynamics for matrix…
Stochastic games are an important class of problems that generalize Markov decision processes to game theoretic scenarios. We consider finite state two-player zero-sum stochastic games over an infinite time horizon with discounted rewards.…
Nash equilibria provide a principled framework for modeling interactions in multi-agent decision-making and control. However, many equilibrium-seeking methods implicitly assume that each agent has access to the other agents' objectives and…
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…
In this paper, we investigate a class of nonzero-sum dynamic stochastic games, where players have linear dynamics and quadratic cost functions. The players are coupled in both dynamics and cost through a linear regression (weighted average)…
In this paper, we address the inverse problem in the case of linear-quadratic discrete-time dynamic non-cooperative games. Given feedback laws of players that are known to be a Nash equilibrium pair for a discrete-time linear system, we…
We derive sublinear-time quantum algorithms for computing the Nash equilibrium of two-player zero-sum games, based on efficient Gibbs sampling methods. We are able to achieve speed-ups for both dense and sparse payoff matrices at the cost…
With increasing game size, a problem of computational complexity arises. This is especially true in real world problems such as in social systems, where there is a significant population of players involved in the game, and the complexity…
This paper investigates closed-loop Nash equilibria for discrete-time linear-quadratic (LQ) stochastic nonzero-sum difference games with random coefficients. Unlike existing works, we consider randomness in both state dynamics and cost…
The designs of many large-scale systems today, from traffic routing environments to smart grids, rely on game-theoretic equilibrium concepts. However, as the size of an $N$-player game typically grows exponentially with $N$, standard game…
In this paper, we consider a linear quadratic stochastic two-person zero-sum differential game. The controls for both players are allowed to appear in both drift and diffusion of the state equation. The weighting matrices in the performance…
In this paper, a Nash-type fictitious game framework is introduced to handle a time-inconsistent linear-quadratic optimal control. The Nash-type game in this framework is called fictitious as it is between the decision maker (called real…
Feedback Nash equilibrium strategies in multi-agent dynamic games require availability of all players' state information to compute control actions. However, in real-world scenarios, sensing and communication limitations between agents make…
We study linear quadratic dynamic games where players are uncertain about each other's control policies or goals and consequently seek to be strategically robust. Building on recent work on strategically robust and risk-averse game theory,…
An open problem in linear quadratic (LQ) games has been characterizing the Nash equilibria. This problem has renewed relevance given the surge of work on understanding the convergence of learning algorithms in dynamic games. This paper…
We introduce a new class of context dependent, incomplete information games to serve as structured prediction models for settings with significant strategic interactions. Our games map the input context to outcomes by first condensing the…
Adversarial multiplayer games are an important object of study in multiagent learning. In particular, polymatrix zero-sum games are a multiplayer setting where Nash equilibria are known to be efficiently computable. Towards understanding…
In this work we consider a stochastic linear quadratic two-player game. The state measurements are observed through a switched noiseless communication link. Each player incurs a finite cost every time the link is established to get…