3. 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 I's accuracy function will be denoted by A1 (t) and Player 2's accuracy function by A2(t). 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 M(x, y, z) be the expected payoff to Player 1 if he shoots at time x and Player 2 shoots his silent bullet at time y and his noisy bullet at time z. Determine M(x, y, z) 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