Shmuel Gal

Search Games with Mobile and Immobile Hider

We consider search games in which the searcher moves along a continuous trajectory in a set Q until he captures the hider, where Q is either a network or a two (or more) dimensional region. We distinguish between two types of games; in the first type which is considered in the first part of the paper, the hider is immobile while in the second type of games which is considered in the rest of the paper, the hider is mobile. A complete solution is presented for some of the games, while for others only upper and lower bounds are given and some open problems associated with those games are presented for further research.

Rendezvous Search on the Line

We present two new results for the asymmetric rendezvous problem on the line. We first show that it is never optimal for one player to be stationary during the entire search period in the two-player rendezvous. Then we consider the meeting time of n-players in the worst case and show that it has an asymptotic behavior of n = 2 + O(log n).

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

Online searching with turn cost

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On the optimality of a simple strategy for searching graphs

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

Optimal Test Design for Reliability Demonstration

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Minimax Solutions for Linear Search Problems

) 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

A Discrete Search Game

6.8\mu.

Participation in auctions

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

A mixed-strategy minimax theorem without compactness

5.7\mu.