Cops and Robber is a pursuit and evasion game played on graphs that has received much attention. We consider an extension of Cops and Robber, distance k Cops and Robber, where the cops win if they are distance at most k from the robber in G. The cop number of a graph G is the minimum number of cops needed to capture the robber in G. The distance k analogue of the cop number, written ck(G), equa...

System design often explores optimality of performance. What is optimal is, however, often not predefined or static in most cases, because it is affected by the context of operation, such as the environment or external system inputs. In this paper, we formulate the maintenance of optimality of performance in dynamical systems in terms of the standard notion of stabilization. For systems with ob...

This paper shows a method to obtain the exact solution for a missile and an aircraft differential games which minimizes and maximizes the essential pay-off of the problem: the miss distance, without employing any linearized approximation. For this purpose, we introduced the concept of energy maneuverability. Once the families of optimal terminal surfaces are obtained, the proposed method can so...

In contrast to prior disaggregated product level studies on tariff evasion which have focused on select country pairs, we develop a model that allows us to consistently estimate average tariff evasion effects on aggregate bilateral trade data. This has two distinct advantages over prior work. We are able to obtain a more general test for average tariff evasion effects across a large number of c...

This paper presents an algorithm for a visibility-based pursuit-evasion problem in which bounds on the speeds of the pursuer and evader are given. The pursuer tries to find the evader inside of a simply-connected polygonal environment, and the evader in turn tries actively to avoid detection. The algorithm is at least as powerful as the complete algorithm for the unbounded speed case, and with ...

We present an algorithm for a pair of pursuers, each with one rotating beam (flashlight, laser or a camera), searching for an unpredictable, moving target in a 2D environment (simple polygon). Given a polygon with n edges, the algorithm decides in time O(n) whether it can be cleared by the pursuers, and if so, constructs a search schedule. The pursuers are allowed to move on the boundary and in...

We introduce and study the game of " Selfish Cops and Adversarial Robber " (SCAR) which is an N-player generalization of the " classic " two-player cops and robbers (CR) game. We prove that SCAR has a Nash equilibrium in deterministic strategies.

5 We study pursuit-evasion games in which a pursuer tries to capture an evader by moving on to the 6 evader’s current location. We investigate how sensing capability of the pursuer affects the game outcome. 7 In particular, we consider a pursuer which can sense only the bearing to an evader. Furthermore, there 8 is noise in the measurements in such a way that an adversary may adjust each bearin...

We prove that the robber can evade (that is, stay at least unit distance from) at least bn/5.889c cops patroling an n × n continuous square region, that a robber can always evade a single cop patroling a square with side length 4 or larger, and that a single cop on patrol can always capture the robber in a square with side length smaller than 2.189 · · · .