Related papers: Operator-Theoretic Methods for Differential Games
The Koopman Operator (KO) takes nonlinear state dynamics and ``lifts'' those dynamics to an infinite-dimensional functional space of observables in which those dynamics are linear. Computational applications typically use a…
Traffic scenarios are inherently interactive. Multiple decision-makers predict the actions of others and choose strategies that maximize their rewards. We view these interactions from the perspective of game theory which introduces various…
This letter employs differential game theory to address the defense problem of a circular target area with perception constraints, involving a single defender and a single attacker. The defender is restricted to moving along the perimeter,…
The Koopman Operator (KO) offers a promising alternative methodology to solve ordinary differential equations analytically. The solution of the dynamical system is analyzed in terms of observables, which are expressed as a linear…
An operational relevant conflict between teams of autonomous vehicles in the Beyond Visual Range domain is addressed in this paper. Optimal strategies are designed in order for a team of air interceptors to protect a high value asset and…
Dynamic games arise when multiple agents with differing objectives choose control inputs to a dynamic system. Dynamic games model a wide variety of applications in economics, defense, and energy systems. However, compared to single-agent…
The paper is concerned with a zero-sum continuous-time stochastic differential game with a dynamics controlled by a Markov process and a terminal payoff. The value function of the original game is estimated using the value function of a…
A defender-attacker-target problem with non-moving target is considered. This problem is modeled by a pursuit-evasion zero-sum differential game with linear dynamics and quadratic cost functional. In this game the pursuer is the defender,…
Game theory offers an interpretable mathematical framework for modeling multi-agent interactions. However, its applicability in real-world robotics applications is hindered by several challenges, such as unknown agents' preferences and…
A fundamental task in mobile robotics is to keep an agent under surveillance using an autonomous robotic platform equipped with a sensing device. Using differential game theory, we study a particular setup of the previous problem. A…
Cooperatively planning for multiple agents has been proposed as a promising method for strategic and motion planning for automated vehicles. By taking into account the intent of every agent, the ego agent can incorporate future interactions…
The Koopman Operator (KO) is a mathematical construct that maps nonlinear (state space) dynamics to corresponding linear dynamics in an infinite-dimensional functional space. For practical applications, finite-dimensional approximations can…
Motivated by a vaccination coverage problem, we consider here a zero-sum differential game governed by a differential system consisting of a hyperbolic partial differential equation (PDE) and an ordinary differential equation (ODE). Two…
Zero-determinant strategies are a class of strategies in repeated games which unilaterally control payoffs. Zero-determinant strategies have attracted much attention in studies of social dilemma, particularly in the context of evolution of…
The purpose of this paper is to study 2-person zero-sum stochastic differential games, in which one player is a major one and the other player is a group of $N$ minor agents which are collectively playing, statistically identical and have…
In this work we propose a kinetic formulation for evolutionary game theory for zero sum games when the agents use mixed strategies. We start with a simple adaptive rule, where after an encounter each agent increases the probability of play…
We consider an autonomous navigation problem, whereby a traveler aims at traversing an environment in which an adversary tries to set an ambush. A two players zero sum game is introduced. Players' strategies are computed as random path…
Solutions to pursuit-evasion and surveillance-evasion differential games are typically computed and expressed using open-loop representations, with the synthesis of feedback strategies significantly less common. We propose a numerical…
The Distributional Koopman Operator (DKO) is introduced as a way to perform Koopman analysis on random dynamical systems where only aggregate distribution data is available, thereby eliminating the need for particle tracking or detailed…
Solving strategic games with huge action space is a critical yet under-explored topic in economics, operations research and artificial intelligence. This paper proposes new learning algorithms for solving two-player zero-sum normal-form…