Related papers: Feedback and Open-Loop Nash Equilibria for LQ Infi…
Dynamic games provide a fundamental framework for multi-agent decision-making over time, yet computing feedback Nash equilibria (FNEs) in infinite-horizon discrete-time linear-quadratic (LQ) settings remains computationally challenging.…
Dynamic games offer a versatile framework for modeling the evolving interactions of strategic agents, whose steady-state behavior can be captured by the Nash equilibria of the games. Nash equilibria are often computed in feedback, with…
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.…
Considering linear-quadratic discrete-time games with unknown input/output/state (i/o/s) dynamics and state, we provide necessary and sufficient conditions for the existence and uniqueness of feedback Nash equilibria (FNE) in the…
Non-cooperative dynamic game theory provides a principled approach to modeling sequential decision-making among multiple noncommunicative agents. A key focus has been on finding Nash equilibria in two-agent zero-sum dynamic games under…
Considering infinite-horizon, discrete-time, linear quadratic, N-player dynamic games with scalar dynamics, a graphical representation of feedback Nash equilibrium solutions is provided. This representation is utilised to derive conditions…
Finite-horizon linear quadratic (LQ) games admit a unique Nash equilibrium, while infinite-horizon settings may have multiple. We clarify the relationship between these two cases by interpreting the finite-horizon equilibrium as a nonlinear…
For the characterization of Feedback Nash Equilibria (FNE) in linear quadratic games, this paper provides a detailed analysis of the discrete-time discounted coupled best-response equations for the scalar two-player setting, together with a…
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…
Game-theoretic approaches and Nash equilibrium have been widely applied across various engineering domains. However, practical challenges such as disturbances, delays, and actuator limitations can hinder the precise execution of Nash…
We present the concept of a Generalized Feedback Nash Equilibrium (GFNE) in dynamic games, extending the Feedback Nash Equilibrium concept to games in which players are subject to state and input constraints. We formalize necessary and…
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…
In this paper, we study a class of two-player deterministic finite-horizon difference games with coupled inequality constraints, where each player has two types of decision variables: one involving sequential interactions and the other…
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…
Trajectory planning for autonomous race cars poses special challenges due to the highly interactive and competitive environment. Prior work has applied game theory as it provides equilibria for such non-cooperative dynamic problems. This…
This paper develops a predictive compensation framework for finite-horizon, discrete-time linear quadratic dynamic games subject to Gauss-Markov execution deviations from feedback Nash strategies. One player's control is corrupted by…
We identify structural assumptions which provide solvability of the Nash system arising from a linear-quadratic closed-loop game, with stable properties with respect to the number of players. In a setting of interactions governed by a…
Interaction-aware trajectory planning is crucial for closing the gap between autonomous racing cars and human racing drivers. Prior work has applied game theory as it provides equilibrium concepts for non-cooperative dynamic problems. With…
We study the global convergence of policy optimization for finding the Nash equilibria (NE) in zero-sum linear quadratic (LQ) games. To this end, we first investigate the landscape of LQ games, viewing it as a nonconvex-nonconcave…
In this paper we propose a numerical method to obtain an approximation of Nash equilibria for multi-player non-cooperative games with a special structure. We consider the infinite horizon problem in a case which leads to a system of…