Related papers: Best Laid Plans of Lions and Men
This paper is concerned with continuous-time pursuit and evasion games. Typically, we have a lion and a man in a metric space: they have the same speed, and the lion wishes to catch the man while the man tries to evade capture. We are…
We consider the following game played in the Euclidean plane: There is any countable set of unit speed lions and one fast man who can run with speed $1+\varepsilon$ for some value $\varepsilon>0$. Can the man survive? We answer the question…
The pursuit-evasion game with two persons is considered. Both players are moving in a metric space, have equal maximum speeds and complete information about the location of each other. We study the sufficient conditions for a capture (with…
A lion and a man move continuously in a space $X$. The aim of the lion is to capture his prey while the man wants to escape forever. Which of them has a strategy? This question has been studied for different metric domains. In this article…
Suppose an escaping player ("human") moves continuously at maximum speed $1$ in the interior of a region, while a pursuing player ("zombie") moves continuously at maximum speed $r$ outside the region. For what $r$ can the first player…
In this paper we analyze, based on an interplay between ideas and techniques from logic and geometric analysis, a pursuit-evasion game. More precisely, we focus on a uniform betweenness property and use it in the study of a discrete lion…
Something is definitely wrong. If the game has a linear winning strategy, then it is tractable. What's going on? Well, we describe a two-person game which has a definite winner, that is, a player who can force a win in a finite number of…
This paper focuses on the relation between the fixed point property for continuous mappings and a discrete lion and man game played in a strongly convex domain. Our main result states that in locally compact geodesic spaces, the compactness…
As avid anglers we were always interested in the survival chances of fish in turbulent oceans. This paper addresses this question mathematically. We show that a fish with bounded aquatic locomotion speed can reach any point in the ocean if…
We study the capture of a diffusing "lamb" by diffusing "lions" in one dimension. The capture dynamics is exactly soluble by probabilistic techniques when the number of lions is very small, and is tractable by extreme statistics…
We study computability-theoretic aspects of differential games. Our focus is on pursuit and evasion games played in Euclidean spaces in the tradition of Rado's "Lion versus Man" game. In some ways, these games can be viewed as continuous…
In this paper, a novel lion strategy for David Gale's lion and man problem is proposed. The devised approach enhances a popular strategy proposed by Sgall, which relies on the computation of a suitable "center". The key idea of the new…
Mortality is an instrument of natural selection. Evolutionary motivated theories imply its irreversibility and life history dependence. This is inconsistent with mortality data for protected populations. Accurate analysis yields mortality…
In the paper by D.~Burago, S.~Ivanov and A.~Novikov, "A survival guide for feeble fish", it has been shown that a fish with limited velocity can reach any point in the (possibly unbounded) ocean provided that the fluid velocity field is…
A general form of the Lions-Magenes theorems on solvability of an elliptic boundary-value problem in the spaces of nonregular distributions is proved. We find a general condition on the space of right-hand sides of the elliptic equation…
We consider the Lion and Man game, i.e., a two-person pursuit-evasion game with equal players' top speeds. We assume that capture radius is positive and chosen in advance. The main aim of the paper is describing pursuer's winning strategies…
Infinite games where several players seek to coordinate under imperfect information are known to be intractable, unless the information flow is severely restricted. Examples of undecidable cases typically feature a situation where players…
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…
We propose two models of the evolution of a pair of competing populations. Both are lattice based. The first is a compromise between fully spatial models, which do not appear amenable to analytic results, and interacting particle system…
We study two-player reachability games on finite graphs. At each state the interaction between the players is concurrent and there is a stochastic Nature. Players also play stochastically. The literature tells us that 1) Player B, who wants…