Network games have been instrumental in understanding strategic behaviors over networks for applications such as critical infrastructure networks, social networks, and cyber-physical systems. One critical challenge of network games is that the behaviors of the players are constrained by the underlying physical laws or safety rules, and the players may not have complete knowledge of network-wide constraints. To this end, this paper proposes a game framework to study constrained games on networks, where the players are locally aware of the constraints. We use \textit{awareness levels} to capture the scope of the network constraints that players are aware of. We first define and show the existence of generalized Nash equilibria (GNE) of the game, and point out that higher awareness levels of the players would lead to a larger set of GNE solutions. We use necessary and sufficient conditions to characterize the GNE, and propose the concept of the dual game to show that one can convert a locally-aware constrained game into a two-layer unconstrained game problem. We use linear quadratic games as case studies to corroborate the analytical results, and in particular, show the duality between Bertrand games and Cournot games.%, where each layer comprises an unconstrained game.
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. They model a wide range of applications including economics, defense, and energy systems. We show how to exploit the temporal structure in projected gradient and Douglas-Rachford (DR) splitting methods. The resulting algorithms converge locally to open-loop Nash equilibria (OLNE) at linear rates. Furthermore, we extend stagewise Newton method to find a local f…
This paper studies an $N$--agent cost-coupled game where the agents are connected via an unreliable capacity constrained network. Each agent receives state information over that network which loses packets with probability $p$. A Base station (BS) actively schedules agent communications over the network by minimizing a weighted Age of Information (WAoI) based cost function under a capacity limit $\mathcal{C} < N$ on the number of transmission attempts at each instant. Under a standard information structure, we show that the problem can be decoupled into a scheduling problem for the BS and a ga…
This paper presents Hamilton-Jacobi (HJ) formulations for two classes of two-player zero-sum games: one with a maximum cost value over time, and one with a minimum cost value over time. In the zero-sum game setting, player A minimizes the given cost while satisfying state constraints, and player B wants to prevent player A's success. For each class of problems, this paper presents two HJ equations: one for time-varying dynamics, cost, and state constraint; the other for time-invariant dynamics, cost, and state constraint. Utilizing the HJ equations, the optimal control for each player is analy…
In this paper, we study a Target-Attacker-Defender (TAD) differential game involving one attacker, one target and multiple defenders. We consider two variations where (a) the attacker and the target have unlimited observation range and the defenders are visibility constrained (b) only the attacker has unlimited observation range and the remaining players are visibility constrained. We model the players' interactions as a dynamic game with asymmetric information. Here, the visibility constraints of the players induce a visibility network which encapsulates the visibility information during the …
Considering uncertainties and disturbances is an important, yet challenging, step in successful decision making. The problem becomes more challenging in safety-constrained environments. In this paper, we propose a robust and safe trajectory optimization algorithm through solving a constrained min-max optimal control problem. The proposed method leverages a game theoretic differential dynamic programming approach with barrier states to handle parametric and non-parametric uncertainties in safety-critical control systems. Barrier states are embedded into the differential game's dynamics and cost…
Learning processes in games explain how players grapple with one another in seeking an equilibrium. We study a natural model of learning based on individual gradients in two-player continuous games. In such games, the arguably natural notion of a local equilibrium is a differential Nash equilibrium. However, the set of locally exponentially stable equilibria of the learning dynamics do not necessarily coincide with the set of differential Nash equilibria of the corresponding game. To characterize this gap, we provide formal guarantees for the stability or instability of such fixed points by le…
Multi-agent networked control systems (NCSs) are often subject to model uncertainty and are limited by large communication cost, associated with feedback of data between the system nodes. To provide robustness against model uncertainty and to reduce the communication cost, this paper investigates the mixed $H_2/H_{\infty}$ control problem for NCS under the sparsity constraint. First, proximal alternating linearized minimization (PALM) is employed to solve the centralized social optimization where the agents have the same optimization objective. Next, we investigate a sparsity-constrained nonco…
