# John Phillpot

Harvey Mudd College Mathematics 2016

Thesis Advisor: | Prof. Ran Libeskind-Hadas |
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Second Reader: | Prof. Nick Pippenger |

E-Mail: | jphillpot@math.hmc.edu |

## Line-of-sight Pursuit and Evasion Games on Polytopes in Rn

We study single-pursuer, line-of-sight Pursuit and Evasion games in polytopes in Rn. Our ultimate goal is to generalize (or prove inadequate) a pursuer strategy proven to work on a large class of polygons in Rn. The strategy in question, commonly known as the Rook's strategy, has the Pursuer to progress from left to right in the polygon, at each point defending it's ``frontier'' from incursion by the Evader. Previous work shows that this strategy is sufficient in any monotone, scallop, or strictly sweepable polygon. In this report, we generalize the Rook's strategy to monotone, scallop, and strictly sweepable polytopes of arbitrary dimension and analyze its effectiveness in each of these cases.