Suppose in Exercise 19 that whenever the convoy goes overland two soldiers are lost to land mines, whether they are attacked or not. Thus, if the army encounters the guerrillas, there will be 9 casualties. If it does not encounter the guerrillas, here will be 2 casualties.

a. Find the optimal strategies for the army and the guerrillas with respect to the number of army casualties.

b. In part (a), what is the “value” of the game? What does this represent in terms of the troops?

Data From Exercise 19

A certain army is engaged in guerrilla warfare. It has two ways of getting supplies to its troops: it can send a convoy up the river road or it can send a convoy overland through the jungle. On a given day, the guerrillas can watch only one of the two roads. If the convoy goes along the river and the guerrillas are there, the convoy will have to turn back and 4 army soldiers will be lost. If the convoy goes overland and encounters the guerrillas, half the supplies will get through, but 7 army soldiers will be lost. Each day a supply convoy travels one of the roads, and if the guerrillas are watching the other road, the convoy gets through with no losses. Set up and solve the following as matrix games, with R being the army.