A HIDE AND SEEK GAME WITH TRAVELING COST

Abstract

There are n, neighboring cells in a straight line. A man hides among one of all cells and stays there. The searcher examines each cell until he finds the hider. Associated with the examination by the searcher are a traveling cost dependent on the distance from the last cell examined and a fixed examination cost. The searcher wishes to minimize the expectation of cost of finding the hider. On the other hand the hider wishes to maximize it. This is formulated as a two-person zero-sum game and it is solved.