This is a question pertaining to Game Theory, and it has 4 subparts:

Player 1 ("hider") and Player 2 ("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, D. The admin of the game gives player 1 a $100 bill, and player 1 must hide it in one of the four boxes. Player 2 doesn't observe where player 1 hides the $100. Once Player 1 has hidden the bill, Player 2 must open one of the boxes. If the money is in the box that Player 2 opens, Player 2 keeps the $100. If not, Player 1 keeps the $100.

a) Does this game have pure-strategy Nash equilibrium?

b) Find the mixed-strategy Nash equilibrium.

c) Suppose it is common knowledge that Player 1 likes the letter A and would get extra satisfaction from putting the money in box A. Let this satisfaction be equivalent to receiving $20. Assume this is in addition to any money received in the game. How does Player 1's preference for A affect the equilibrium mixing probabilities? Calculate the new equilibrium strategy profile if you can.

d) Describe the equilibria of the game in which Player 1's extra satisfaction from selecting box A is equivalent to receiving $120.