In nickel and dime game a person is odered the choice between a nickel and a dime. If the person takes dime then the game is over, but, if the person takes the nickel then the game is repeated.
a) Suggest the case in which the game is repeated three times at most. Make the tree for this game and the optimal strategy.
b) Assume the game is repeated n times at most. Determine the optimal strategy?
c) Suggest a variant of game in which if the dime is taken the game stops, but if the nickel is taken then game is repeated with probability p. Suppose that p < 1, so the game will eventually stop. Compute the optimal strategy?