Another Mendelsohn game. Two players simultaneously

choose an integer between 1 and n inclusive, where n 5. If the numbers are

equal there is no payout. The player that chooses a number one larger than that

chosen by his opponent wins 2. The player that chooses a number two or more

larger than that chosen by his opponent loses 1. (a) Set up the game matrix.

(b) It turns out that the optimal strategy satises pi > 0 for i = 1; : : : ; 5, and

pi = 0 for all other i. Solve for the optimal p. (It is not too dicult since you

can argue that p1 = p5

and p2 = p4 by symmetry of the equations.) Check that in fact the strategy

you nd is optimal.

The game with matrix A has value zero, and (6/11,3/11, 2/11) is optimal for I.

(a) Find the value of the game with matrix B and an optimal strategy for I.

(b) Find an optimal strategy for II in both games.

(II-47 3). A game without a value.