Don't solve if u can't solve each and every parts 000000000000Exercise 2.13: Challenging Question. Two women, Anna and Bess, claimto be the legal owners of a diamond ring that each claims - has greatsentimental value. Neither of them can produce evidence of ownership andnobody else is staking a claim on the ring. Judge Sabio wants the ring to go tothe legal owner, but he does not know which of the two women is in fact thelegal owner. He decides to proceed as follows. First he announces a fine of $F 0 and then asks Anna and Bess to play the following game.Move 1: Anna moves first. Either she gives up her claim to the ring (in whichcase Bess gets the ring, the game ends and nobody pays the fine) or she assertsher claim, in which case the game proceeds to Move 2.Move 2: Bess either accepts Anna's claim (in which case Anna gets the ring, thegame ends and nobody pays the fine) or challenges her claim. In the latter case,Bess must put in a bid, call it B, and Anna must pay the fine of $F to Sabio. Thegame goes on to Move 3.Move 3: Anna now either matches Bess's bid (in which case Anna gets the ring.Anna pays $B to Sabio in addition to the fine that she already paid - andBess pays the fine of $F to Sabio) or chooses not to match (in which case Bessgets the ring and pays her bid of $B to Sabio and, furthermore, Sabio keeps thefine that Anna already paid).Denote by C, the monetary equivalent of getting the ring for Anna (that is,getting the ring is as good, in Anna's mind, as getting $C) and C, themonetary equivalent of getting the ring for Bess. Not getting the ring isconsidered by both as good as getting zero dollars.(a) Draw an extensive game with perfect information to represent the abovesituation, assuming that there are only two possible bids: B, and B. Writethe payoffs to Anna and Bess next to each terminal node.(b) Find the backward-induction solution of the game you drew in part (a) forthe case where B, C C B F 0.Now consider the general case where the bid B can be any non-negativenumber and assume that both Anna and Bess are very wealthy. Assume alsothat CA, C and F are positive numbers and that CA and C, are commonknowledge between Anna and Bess. We want to show that, at the backward-induction solution of the game, the ring always goes to the legal owner. Sincewe (like Sabio) don't know who the legal owner is, we must consider two cases.Case 1: the legal owner is Anna. Let us assume that this implies that CA CCase 2: the legal owner is Bess. Let us assume that this implies that C CA-(c) Find the backward-induction solution for Case 1 and show that it impliesthat the ring goes to Anna.(d) Find the backward-induction solution for Case 2 and show that it impliesthat the ring goes to Bess.(e) How much money does Sabio make in equilibrium? How much money doAnn and Bess end up paying in equilibrium? (By 'equilibrium' we mean'backward induction solution'.)

Question

Don't solve if u can't solve each and every parts 000000000000Exercise 2.13: Challenging Question. Two women, Anna and Bess, claimto be the legal owners of a diamond ring that each claims - has greatsentimental value. Neither of them can produce evidence of ownership andnobody else is staking a claim on the ring. Judge Sabio wants the ring to go tothe legal owner, but he does not know which of the two women is in fact thelegal owner. He decides to proceed as follows. First he announces a fine of $F> 0 and then asks Anna and Bess to play the following game.Move 1: Anna moves first. Either she gives up her claim to the ring (in whichcase Bess gets the ring, the game ends and nobody pays the fine) or she assertsher claim, in which case the game proceeds to Move 2.Move 2: Bess either accepts Anna's claim (in which case Anna gets the ring, thegame ends and nobody pays the fine) or challenges her claim. In the latter case,Bess must put in a bid, call it B, and Anna must pay the fine of $F to Sabio. Thegame goes on to Move 3.Move 3: Anna now either matches Bess's bid (in which case Anna gets the ring.Anna pays $B to Sabio in addition to the fine that she already paid - andBess pays the fine of $F to Sabio) or chooses not to match (in which case Bessgets the ring and pays her bid of $B to Sabio and, furthermore, Sabio keeps thefine that Anna already paid).Denote by C, the monetary equivalent of getting the ring for Anna (that is,getting the ring is as good, in Anna's mind, as getting $C) and C, themonetary equivalent of getting the ring for Bess. Not getting the ring isconsidered by both as good as getting zero dollars.(a) Draw an extensive game with perfect information to represent the abovesituation, assuming that there are only two possible bids: B, and B. Writethe payoffs to Anna and Bess next to each terminal node.(b) Find the backward-induction solution of the game you drew in part (a) forthe case where B, > C > C > B > F> 0.Now consider the general case where the bid B can be any non-negativenumber and assume that both Anna and Bess are very wealthy. Assume alsothat CA, C and F are positive numbers and that CA and C, are commonknowledge between Anna and Bess. We want to show that, at the backward-induction solution of the game, the ring always goes to the legal owner. Sincewe (like Sabio) don't know who the legal owner is, we must consider two cases.Case 1: the legal owner is Anna. Let us assume that this implies that CA > CCase 2: the legal owner is Bess. Let us assume that this implies that C > CA-(c) Find the backward-induction solution for Case 1 and show that it impliesthat the ring goes to Anna.(d) Find the backward-induction solution for Case 2 and show that it impliesthat the ring goes to Bess.(e) How much money does Sabio make in equilibrium? How much money doAnn and Bess end up paying in equilibrium? (By 'equilibrium' we mean'backward induction solution'.)

Accepted Answer

Backward induction is a game theory technique for solving sequential games. It involves working from…