On search games that include ambush

We present a stochastic game that models ambush/search in a finite region Q which has area but no other structure. The searcher can search a unit area of Q in unit time or adopt an "ambush" mode for a certain period. The searcher "captures" the hider when the searched region contains the hider's location or if the hider moves while the searcher...

A Proof of the Kikuta–Ruckle Conjecture on Cyclic Caching of Resources

Suppose that a hider possesses a continuously divisible resource that he may distribute around a circle. The resources on a random arc in the circle are lost. The hider has a priori information on the length of the arc and he wants to maximize the probability that the retrieved portion exceeds a critical quantity, which is enough to survive on....

On Ruckle's Conjecture on Accumulation Games

In an accumulation game, the Hider secretly distributes his given total wealth $h$ among $n$ locations, while the Searcher picks $r$ locations and confiscates the material placed there. The Hider wins if what is left at the remaining $n-r$ locations is at least 1; otherwise the Searcher wins. Ruckle's conjecture says that an optimal Hider...