Related papers: Inverse linear-quadratic nonzero-sum differential …
The paper is concerned with a zero-sum Stackelberg stochastic linear-quadratic (LQ, for short) differential game over finite horizons. Under a fairly weak condition, the Stackelberg equilibrium is explicitly obtained by first solving a…
We consider two-player non-zero-sum linear-quadratic Gaussian games in which both players aim to minimize a quadratic cost function while controlling a linear and stochastic state process {using linear policies}. The system is partially…
In this paper, we study inverse game theory (resp. inverse multiagent learning) in which the goal is to find parameters of a game's payoff functions for which the expected (resp. sampled) behavior is an equilibrium. We formulate these…
In the present paper, we consider a class of two players infinite horizon differential games, with piecewise smooth costs exponentially discounted in time. Through the analysis of the value functions, we study in which cases it is possible…
We analyze best response dynamics for finding a Nash equilibrium of an infinite horizon zero-sum stochastic linear quadratic dynamic game (LQDG) with partial and asymmetric information. We derive explicit expressions for each player's best…
We study a setting in which two players play a (possibly approximate) Nash equilibrium of a bimatrix game, while a learner observes only their actions and has no knowledge of the equilibrium or the underlying game. A natural question is…
We study a class of deterministic finite-horizon two-player nonzero-sum differential games where players are endowed with different kinds of controls. We assume that Player 1 uses piecewise-continuous controls, while Player 2 uses impulse…
We consider dynamic games with linear dynamics and quadratic objective functions. We observe that the unconstrained open-loop Nash equilibrium coincides with a linear quadratic regulator in an augmented space, thus deriving an explicit…
This paper presents algorithms for non-zero sum nonlinear constrained dynamic games with full information. Such problems emerge when multiple players with action constraints and differing objectives interact with the same dynamic system.…
Many problems in robotics involve multiple decision making agents. To operate efficiently in such settings, a robot must reason about the impact of its decisions on the behavior of other agents. Differential games offer an expressive…
As demonstrated by Ratliff et al. (2014), inverse optimization can be used to recover the objective function parameters of players in multi-player Nash games. These games involve the optimization problems of multiple players in which the…
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 study the problem of repeated play in a zero-sum game in which the payoff matrix may change, in a possibly adversarial fashion, on each round; we call these Online Matrix Games. Finding the Nash Equilibrium (NE) of a two player zero-sum…
We address cost identification in a finite-horizon linear quadratic Gaussian game. We characterize the set of cost parameters that generate a given Nash equilibrium policy. We propose a backpropagation algorithm to identify the time-varying…
We introduce a novel class of Nash equilibrium seeking dynamics for non-cooperative games with a finite number of players, where the convergence to the Nash equilibrium is bounded by a KL function with a settling time that can be upper…
We consider a non-zero-sum linear quadratic Gaussian (LQG) dynamic game with asymmetric information. Each player observes privately a noisy version of a (hidden) state of the world $V$, resulting in dependent private observations. We study…
Ensuring robust decision-making in multi-agent systems is challenging when agents have distinct, possibly conflicting objectives and lack full knowledge of each other's strategies. This is apparent in safety-critical applications such as…
Robots deployed to the real world must be able to interact with other agents in their environment. Dynamic game theory provides a powerful mathematical framework for modeling scenarios in which agents have individual objectives and…
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…
This paper investigates the encirclement control problem involving two groups using a non-cooperative differential game approach. The active group seeks to chase and encircle the passive group, while the passive group responds by fleeing…