A generalization of Ruckle's results for an ambush game
Consider the following 2-person 0-sum normal form game. Player 1 picks a point on \([0,1]\). Simultaneously, player 2 picks two obstacles (intervals of length \(a\) and \(b\), respectively). Player 1 wins (gets payoff \(=+1\)) if the point he or she picked is in neither of player 2's intervals. Let \(k\) be an integer and suppose the following: \(0< a< b< 1/2\), \(kb< 1\leq (k+1)b\). Then for the case \(kb+a\geq 1\) the paper finds conditions under which the value of the game exists and can be expressed in closed form. In particular, the value to player 1 is increasing in \(k\). The results in this paper considerably extend those of \textit{W. H. Ruckle} [Geometric games and their applications, Boston, Pitman (1983; Zbl 0519.90096)].
scientific article; zbMATH DE number 1358202