Suppose a duel is being fought between two duellists where Player 1 has one silent bullet while Player 2 has in his possession two bullets, one of which is silent and the other noisy. Assume that Player 2 will always shoot with his silent bullet first. The players can fire their bullets at any time in [0, 1]. Player 1's accuracy function will be denoted by 1() and Player 2's accuracy function by 2(). A duellist receives a payoff of +1 if he is the only surviving duellist and -1 if he is shot by his opponent. Both players receive 0 if they both survive or neither survives. Let (, , ) be the expected payoff to Player 1 if he shoots at time and Player 2 shoots his silent bullet at time and his noisy bullet at time . Determine (, , ) but do not solve the game. (Hint: Player 2 will always shoot his silent bullet first and he cannot shoot both bullets simultaneously, hence y < z. Consider the following 5 possibilities: x < y < z, x = y < z, y < x < z, y < z < x, y < z = x)