12. Player 1 (the "hider") and player 2 (the "seeker") play the following game. There are four boxes with lids, arranged in a straight line. For convenience, the boxes are labeled A, B, C, and D. The administrator of the game gives player 1 a $100 bill, and player 1 must hide it in one of the four boxes. Player 2 does not observe where player 1 hides the $100 bill. Once player 1 has hidden the bill, player 2 must open one (and only one) of the boxes. If the money is in the box that player 2 opens, then player 2 keeps the $100. If it is not, player 1 gets to keep the $100. a. What are the pure strategy Nash equilibria, if any? b. Is player 1 playing a non-degenerate mixed strategy in Nash equilibrium in which a positive probability to some but not all of their pure strategies possible? What are the mixed-strategy Nash equilibria? d. Suppose it is common knowledge that the Hider likes the letter \"A\" and gets extra satisfaction from putting the money in box A. Let this satisfaction = receiving $p, where 0