Search Games on Hypergraphs

The main motivation behind this thesis is a certain type of win-lose games that are played on hypergraphs and can be translated into the following puzzle. Suppose there are two persons, say Alice and Bob. There are n biscuits, where n is a positive integer, and Alice chooses s of them uniformly at random. Bob possesses h grams of poison, where h...

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....