Related papers: Lion and Man Game in Compact Spaces

We propose a decentralized solution for a pursuit-evasion game involving a heterogeneous group of rational (selfish) pursuers and a single evader based on the framework of potential games. In the proposed game, the evader aims to delay (or,…

We consider a pursuit-evasion differential game with a Hybrid system of dynamics in Hilbert space with integral constraints on the control functions of players. We show that the pursuer has a winning strategy.

The two main results of this work are the following: if a space $X$ is such that player II has a winning strategy in the game $\gone(\Omega_x, \Omega_x)$ for every $x \in X$, then $X$ is productively countably tight. On the other hand, if a…

Two random processes X and Y on a metric space are said to be $\varepsilon$-shy coupled if there is positive probability of them staying at least a positive distance $\varepsilon$ apart from each other forever. Interest in the literature…

This paper studies a 3D multiplayer reach-avoid differential game with a goal region and a play region. Multiple pursuers defend the goal region by consecutively capturing multiple evaders in the play region. The players have heterogeneous…

This paper studies a target-defense game played between a slow defender and a fast attacker. The attacker wins the game if it reaches the target while avoiding the defender's capture disk. The defender wins the game by preventing the…

We study pursuit-evasion differential games between a faster pursuer moving in 3D space and an evader moving in a plane. We first extend the well-known Apollonius circle to 3D space, by which we construct the isochron for the considered two…

This paper considers a reach-avoid differential game in three-dimensional space with four equal-speed players. A plane divides the game space into a play subspace and a goal subspace. The evader aims at entering the goal subspace while…

Positional games are a well-studied class of combinatorial game. In their usual form, two players take turns to play moves in a set (`the board'), and certain subsets are designated as `winning': the first person to occupy such a set wins…

The optimal strategies to catch a randomly walking cat in various environments are presented. All games have a player that opens a box at step $i$. If the cat is in this box the player wins, if not, the cat moves randomly to an adjacent…

This paper introduced a pursuit and evasion game to be played on a connected graph. One player moves invisibly around the graph, and the other player must guess his position. At each time step the second player guesses a vertex, winning if…

Let S be a topological property of sequences (such as, for example, "to contain a convergent subsequence" or "to have an accumulation point"). We introduce the following open-point game OP(X,S) on a topological space X. In the n'th move,…

Projection games constitute an important class of nonlocal games where, for any answer from the first player, there is a unique correct answer for the second player. This class of games captures nonlocal games arising from constraint…

We study a pursuit-evasion problem which can be viewed as an extension of the keep-away game. In the game, pursuer(s) will attempt to intersect or catch the evader, while the evader can visit a fixed set of locations, which we denote as the…

Shmuel Gal and Jerome Casas have recently introduced a game theoretic model that combines search and pursuit by a predator for a prey animal. The prey (hider) can hide in a finite number of locations. The predator (searcher) can inspect any…

Winning sets of Schmidt's game enjoy a remarkable rigidity. Therefore, this game (and modifications of it) have been applied to many examples of complete metric spaces (X, d) to show that the set of "badly approximable points", with respect…

We consider a pursuit-evasion scenario involving a group of pursuers and a single evader in a two-dimensional unbounded environment. The pursuers aim to capture the evader in finite time while ensuring the evader remains enclosed within the…

This paper studies a two-player game with a quantitative surveillance requirement on an adversarial target moving in a discrete state space and a secondary objective to maximize short-term visibility of the environment. We impose the…

Consider a two-person zero-sum search game between a hider and a searcher. The hider hides among $n$ discrete locations, and the searcher successively visits individual locations until finding the hider. Known to both players, a search at…

In classical works on a planar differential pursuit-evasion game with a faster pursuer, the intercept point resulting from the equilibrium strategies lies on the Apollonius circle. This property was exploited for the construction of the…