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This paper considers for the first time pursuit-evasion (PE) differential games with irrational perceptions of both pursuer and evader on probabilistic characteristics of environmental uncertainty. Firstly, the irrational perceptions of…
We develop a flexible stochastic approximation framework for analyzing the long-run behavior of learning in games (both continuous and finite). The proposed analysis template incorporates a wide array of popular learning algorithms,…
This paper develops an analytical strategy for solving the linear quadratic pursuit-evasion game in arbitrary Keplerian reference orbits. The motion of the pursuer and evader is described using the controlled Tschauner-Hempel equations, and…
Objective: In a companion paper, we propose a parametric hybrid automaton model and an algorithm for the online synthesis of robustly correct and near-optimal controllers for cyber-physical system with reach-avoid guarantees. A key part of…
This paper is about a set-based computing method for solving a general class of two-player zero-sum Stackelberg differential games. We assume that the game is modeled by a set of coupled nonlinear differential equations, which can be…
Quantitative games are two-player zero-sum games played on directed weighted graphs. Total-payoff games (that can be seen as a refinement of the well-studied mean-payoff games) are the variant where the payoff of a play is computed as the…
Game theory is playing more and more important roles in understanding complex systems and in investigating intelligent machines with various uncertainties. As a starting point, we consider the classical two-player zero-sum linear-quadratic…
Simple stochastic games are turn-based 2.5-player zero-sum graph games with a reachability objective. The problem is to compute the winning probability as well as the optimal strategies of both players. In this paper, we compare the three…
We formulate and analyze game-theoretic problems for systems governed by integral equations. For Volterra integral equations, we obtain and prove necessary and sufficient conditions for linear-quadratic problems, and for problems that are…
For the task of moving a set of indistinguishable agents on a connected graph with unit edge distance to an arbitrary set of goal vertices, free of collisions, we propose a fast distance optimal control algorithm that guides the agents into…
The timing of strategic exit is one of the most important but difficult business decisions, especially under competition and uncertainty. Motivated by this problem, we examine a stochastic game of exit in which players are uncertain about…
We lay out a general method for computing branching distances between labeled transition systems. We translate the quantitative games used for defining these distances to other, path-building games which are amenable to methods from the…
Pursuit-evasion is a multi-agent sequential decision problem wherein a group of agents known as pursuers coordinate their traversal of a spatial domain to locate an agent trying to evade them. Pursuit evasion problems arise in a number of…
Reachability games are two-player games played on a graph, where the objective of $\texttt{REACH}$ player is to reach the target set whereas the objective of $\texttt{SAFE}$ player is to stay away from the target set. Reachability games…
Evacuation planning is an essential part of disaster management where the goal is to relocate people under imminent danger to safety. However, finding jointly optimal evacuation routes and schedule that minimizes the average evacuation time…
This paper provides an efficient computational scheme to handle general security games from an adversarial risk analysis perspective. Two cases in relation to single-stage and multi-stage simultaneous defend-attack games motivate our…
We consider a two player game, where a first player has to install a surveillance system within an admissible region. The second player needs to enter the the monitored area, visit a target region, and then leave the area, while minimizing…
This work considers designing an unmanned target hunting system for a swarm of unmanned underwater vehicles (UUVs) to hunt a target with high maneuverability. Differential game theory is used to analyze combat policies of UUVs and the…
End-effector trajectory tracking algorithms find joint motions that drive robot manipulators to track reference trajectories. In practical scenarios, anytime algorithms are preferred for their ability to quickly generate initial motions and…
We develop a martingale approach for studying continuous-time stochastic differential games of control and stopping, in a non-Markovian framework and with the control affecting only the drift term of the state-process. Under appropriate…