Question: The Game of Morra. Two players simultaneously throw out one or two fingers and call out their guess as to what the total sum of the outstretched fingers will be. If a player guesses right, but his opponent does not, he receives payment equal to his guess. In all other cases, it is a draw.
(a) List the pure strategies for this game.
(b) Write down the payoff matrix for this game.
(c) Formulate the row player's problem as a linear programming problem.
(Hint: Recall that the row player's problem is to minimize the maximum expected payout.)
(d) What is the value of this game?
(e) Find the optimal randomized strategy.