On a ruckle problem in discrete games of ambush

Abstract

The following zero-sum game is considered. Red chooses in integer interval [ 1, n ] two integer intervals consisting of k and m points where k + m < n, and Blue chooses an integer point in [1, n]. The payoff to Red equals 1 if the point chosen by Blue is at least in one of the intervals chosen by Red, and 0 otherwise. This work complements the results obtained by Ruckle, Baston and Bostock, and Lee.