Search Games on a Broken Wheel With Traveling and Search Costs

Abstract

The authors analyse a search game involving an immobile hider and a searcher in which play takes place in discrete time on a network comprising a cycle together with a node 0 adjacent to a specified set of nodes in the cycle. The hider chooses a node of the cycle. Unaware of the hider's choice, the searcher starts at the node 0 and, at each subsequent time instant, moves from the node he occupies to an adjacent node and decides whether to search it. Play terminates when the searcher is at the node chosen by the hider and searches there. The searcher incurs a cost of one in moving from a node to an adjacent one and a search cost depending on whether or not the node is in the specified set. The searcher wants to minimize the costs of finding the hider and the hider to maximize them. We obtain upper bounds for the value of this game for the cases when the specified set has no adjacent nodes and when it is an interval. We show that these upper bounds are the value of the game in a number of cases.