Rabbit and hunter game: Two discrete stochastic formulations
type: Item
instance of: scholarly article
title: Rabbit and hunter game: Two discrete stochastic formulations
zbMATH Open document ID: 0623.90105
DOI: 10.1016/0898-1221(87)90105-2
author: A.-L. Colomb
author: Pierre Bernhard
author: George P. Papavassilopoulos
publication date: 1987-01-01T00:00:00Z
review text: This work concerns different versions of the same basic game. A rabbit R can move back and forth along a finite wall in a discrete world \(\{\) 1, 2,..., \(N\}=I_ N\). If \(x_ t\in I_ N\) is the position of R at time t, and \(u_ t\) its jump at time t, the dynamics of R are simply \(x_{t+1}=x_ t+u_ t\). A Hunter H tries to shoot it at each discrete time. If \(v_ t\in I_ N\) is the position at which H aims at time t the two first versions suppose that the bullet reaches the wall in one step of time, so a bullet hits the wall at \(Z_ t\) at time t with \(Z_{t+1}=v_ t\). Capture is defined by \(t_ 1=\inf (t|\) \(x_ t=Z_ t)\). The third version assumes that the bullet takes several time steps to reach the wall. Mixed strategies for H and R are introduced and so \(t_ 1\) is a stopping time. In the first model the payoff that H (resp. R) looks for minimize (resp. maximize) is \(E(t_ 1)\). In the second and third models a fixed time T is given when the game warden forces the hunter to leave, and the payoff is then \(P(t_ 1\leq T)\) that of course H (resp. R) tries to maximize (resp. minimize). In these three models, the authors prove the existence of value and saddle points, and give algorithms to calculate them.
Mathematics Subject Classification ID: 91A24
Mathematics Subject Classification ID: 91A60
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 91A15
zbMATH DE Number: 4012366
zbMATH Keywords: computation of solutions
zbMATH Keywords: Markovian matrix
zbMATH Keywords: Mixed strategies
zbMATH Keywords: value
zbMATH Keywords: saddle points
zbMATH Keywords: algorithms
reviewed by: J.-P. Lepeltier
MaRDI profile type: Publication
full work available at URL: 0898-1221(87)90105-2
OpenAlex ID: W2066901459
cites work: Differential Search Games with Mobile Hider
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 4012366