Vic Baston

Rendezvous on the Line when the Players' Initial Distance is Given by an Unknown Probability Distribution

Two players A and B are randomly placed on a line. The distribution of the distance between them is unknown except that the expected initial distance of the (two) players does not exceed some constant

A generalized inspection game

\mu.

A search game with a protector

The players can move with maximal velocity 1 and would like to meet one another as soon as possible. Most of the paper deals with the asymmetric rendezvous in which each player can use a different trajectory. We find rendezvous trajectories which are efficient against all probability distributions in the above class. (It turns out that our trajectories do not depend on the value of

An Ambush Game with an Unknown Number of Infiltrators

\mu.

Rendezvous on a Planar Lattice

) We also obtain the minimax trajectory of player A if player B just waits for him. This trajectory oscillates with a geometrically increasing amplitude. It guarantees an expected meeting time not exceeding

Search games on networks with travelling and search costs and with arbitrary searcher starting points

6.8\mu.

Technical Note---An Ambush Game with a Fat Infiltrator

We show that, if player B also moves, then the expected meeting time can be reduced to

Search games on a network with travelling and search costs

5.7\mu.

Generalizations in the linear search problem

The expected meeting time can be further reduced if the players use mixed strategies. We show that if player B rests, then the optimal strategy of player A is a mixture of geometric trajectories. It guarantees an expected meeting time not exceeding

Discrete hamstrung squad car games

4.6\mu.