1)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.

a. What is the optimal strategy for the army if it wants to maximize the amount of supplies it gets to its troops? What is the optimal strategy for the guerrillas if they want to prevent the most supplies from getting through? If these strategies are followed, what portion of the supplies gets through?

b. What is the optimal strategy for the army if it wants to minimize its casualties? What is the optimal strategy for the guerrillas if they want to inflict maximum losses on the army? If these strategies are followed, what portion of the supplies gets through?

2)mark each statement True or False. Justify each answer.

a. The payoff matrix for a matrix game indicates what R wins for each combination of moves.

b. With a pure strategy, a player makes the same choice each time the game is played.

c. The value v.x/ of a particular strategy x to player R is equal to the maximum of the inner product of x with each of the columns of the payoff matrix.

d. The Minimax Theorem says that every matrix game has a solution.

e. If row s is recessive to some other row in payoff matrix A, then row s will not be used (that is, have probability zero) in an optimal strategy for (row) player R.