Search and evasion games
Schroeder, Roger Glenn
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This research was part of the author's Ph. D. dissertation. The dissertation advisor, Dr. A. Charnes of Northwestern University, offered valuable advice and guidance. In addition, this work was undertaken while the author participated in the U. S. Naval Junior Line Officer Advanced Scientific Educational Program.","We develop some two-person zero-sum game formulations of search and evasion problems. By employing a game theoretic approach, we allow the hider, as well as the searcher, to choose a strategy. This is in contrast to most search models which assume a stationary or passive hider. Both non-sequential. and sequential search games are investigated. Some interesting aspects of the non- sequential game and an example of an antisubmarine search problem are given. The sequential games consist of a sequence of moves. When the players move, they not only determine a payoff but also the probability that the game terminates before the next move. When at most a finite number of moves is allowed, we prove that a solution may be found by solving a recursive sequence of matrix games. When the number of moves is not bounded, the game is characterized by a special type of non-linear program. The solution to this program can be approximated by successive perturbations of a related linear program. Finally, we obtain the result that a pair of strategies minimaxes the expected duration of the game if and only if these strategies also maximin the probability of termination in one step.
This research was part of the author's Ph. D. dissertation. The dissertation advisor, Dr. A. Charnes of Northwestern University, offered valuable advice and guidance. In addition, this work was undertaken while the author participated in the U. S. Naval Junior Line Officer Advanced Scientific Educational Program.
NPS Report NumberNaval Postgraduate School (U.S.) Technical report/Research paper ; no. 68.
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