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. ISSN 0363-0129

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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
Divisions:	Faculty of Social Sciences > Warwick Business School > Operational Research & Management Sciences Faculty of Social Sciences > Warwick Business School
Journal or Publication Title:	SIAM Journal on Control and Optimization
Publisher:	Society for Industrial and Applied Mathematics
ISSN:	0363-0129
Date:	2008
Volume:	Vol.47
Number:	No.3
Page Range:	pp. 1178-1190
Identification Number:	10.1137/060672054
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
URI:	http://wrap.warwick.ac.uk/id/eprint/50845

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