Optimal Pursuit Strategies for the Lion.
STANFORD UNIV CALIF DEPT OF STATISTICS
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Given a lion L and a man M moving in a circular arena with constant speeds 1 and omega 1, respectively How closely can L approach M and can he achieve a minimum distance. Besicovitch shows that L can get arbitrarily close to M but can never catch M when omega 1. In a previous report the author formulated the problem as a differential game, demonstrated that it has a value rho primed constructed upper and lower bounds on rho primed and determined an optimal evasion strategy for M. The main result is that the following strategy is optimal for L. Move to the center O. Then stay on the radial line OM and head toward M until time 21 log omega. The resulting position is either one where LM or rho primed or one from which L can force LM strictly below rho prime in a finite time. Hence for the ease of unequal speeds the lion can achieve a minimum distance. Author
- Operations Research