A game of group pursuit in which players move on a plane with bounded velocities is considered. The game is supposed to be a nonzerosum simple pursuit game between an evader and m pursuers acting independent of each other. The case of complete information is studied. In other words, each player, choosing control variables at each time instant t > 0, knows the moment t and his own as well as all...

The game of cops and robber, introduced by Nowakowski and Winkler in 1983, is played by two players on a graph G, one controlling k cops and the other one robber, all positioned on VG. The players alternate in moving their pieces to distance at most 1 each. The cops win if they capture the robber, the robber wins by escaping indefinitely. The copnumber of G, that is the smallest k such that k c...

In proof-of-payment transit systems, passengers are legally required to purchase tickets before entering but are not physically forced to do so. Instead, patrol units move about the transit system, inspecting the tickets of passengers, who face fines if caught fare evading. The deterrence of fare evasion depends on the unpredictability and effectiveness of the patrols. In this paper, we present...

We address an on-line version of the visibility-based pursuit-evasion problem. We take a minimalist approach in modeling the capabilities of a pursuer robot. A point pursuer moves in an unknown, simplyconnected, piecewise-smooth planar environment, and is given the task of locating any unpredictable, moving evaders that have unbounded speed. The evaders are assumed to be points that move contin...

A pursuit-evasion differential game of countably many pursuers and one evader is investigated. Integral constraints are imposed on the control functions players. Duration fixed, payoff functional greater lower bound distances between when completed. The want to minimize, maximize payoff. In this paper, we find value construct optimal strategies for

We study a pursuit-evasion game in which one or more cops try to capture a robber by moving onto the robber’s current location. All players have equal maximum velocities. They can observe each other at all times. We show that three cops can capture the robber in any polygonal environment (which can contain any finite number of holes).