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The "Princess and Monster" game on an interval
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Alpern, Steve, Fokkink, Robbert, Lindelauf, Roy and Olsder, Geert-Jan (2008) The "Princess and Monster" game on an interval. SIAM Journal on Control and Optimization, Vol.47 (No.3). pp. 1178-1190. doi:10.1137/060672054 ISSN 0363-0129.
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Official URL: http://dx.doi.org/10.1137/060672054
Abstract
A minimizing searcher S and a maximizing hider H move at unit speed on a closed interval until the first (capture, or payoff) time $T=\min \{ t:S(t)=H(t)\}$ that they meet. This zero-sum princess and monster game or less colorfully search game with mobile hider was proposed by Rufus Isaacs for general networks $Q.$ While the existence and finiteness of the value $V=V(Q)$ has been established for such games, only the circle network has been solved (value and optimal mixed strategies). It seems that the interval network $Q=[-1,1]$ had not been studied because it was assumed to be trivial, with value $3/2$ and “obvious” searcher mixed strategy going equiprobably from one end to the other. We establish that this game is in fact nontrivial by showing that $V<3/2.$ Using a combination of continuous and discrete mixed strategies for both players, we show that $15/11\leq V\leq 13/9.$ The full solution of this very simple game is still open and appears difficult, though many properties of the optimal strategies are derived here.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Social Sciences > Warwick Business School > Operational Research & Management Sciences Faculty of Social Sciences > Warwick Business School |
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Journal or Publication Title: | SIAM Journal on Control and Optimization | ||||
Publisher: | Society for Industrial and Applied Mathematics | ||||
ISSN: | 0363-0129 | ||||
Official Date: | 2008 | ||||
Dates: |
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Volume: | Vol.47 | ||||
Number: | No.3 | ||||
Page Range: | pp. 1178-1190 | ||||
DOI: | 10.1137/060672054 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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