3. A $100 gift card is being auctioned off to Ann and Brandon. Ann has $99 while Brandon has $200. Each bidder will separately write down how much they are willing to pay for the gift card. They cannot bid more money than what they have, and only whole number bids are permitted, i.e., bids can be $0,$1,$2, etc. The highest bidder wins the gift card and pays his/her bid. The lowest bidder gets nothing and pays nothing. If the two bidders tie, they each get the gift card with probability half, in which case the one who gets the card pays his/her bid. For example, if both bid $5, then Ann's average payoff would be while Brandon's average payoff would be (a) Given a profile of pure strategies (s1,s2), what is Ann's payoff UA(s1,s2) ? What is Brandon's payoff UB(s1,s2) ? (b) Show Ann does not have a strictly dominated strategy in this game. (c) For Brandon, show that any bid sB100 is a strictly dominated strategy. (d) Is there a dominant strategy equilibrium? (e) Derive Ann's (pure strategy) best response function BRA(sB) as a function of Brandon's pure strategy sB. (f) Derive Brandon's (pure strategy) best response function BRB(sA) as a function of Ann's pure strategy sA. (g) Find all pure strategy Nash equilibria of this game