.\'il T-Mobile 12:11 PM moodle.umass.edu ECON w9 PROBLEM SET 4 Due by beginning
ID: 1112467 • Letter: #
Question
.'il T-Mobile 12:11 PM moodle.umass.edu ECON w9 PROBLEM SET 4 Due by beginning ef class on Tuesday, Nember 28th. Pleave refer to the sylabus for ate submissien policy. Can be submitted in digital form or as hard copy: . Hard copies ca. be submitted either in class or to Professor Soslu's etlice Crotty Hall #213) on or .If you cannot make it to class on the due date, you can seed a digital copy by the beginning of class Do not sead photos Scan your decument using before the due date. (You can slide year homework under the deor Nace that if you send your copy a ter class, it will be considered as late and·ot be accepted. Digital copies can be sent te a scanner or your phone and send a pdf copy(There are free scanning applications for your phot The one I know of is Genius Scan, but there are many others too Yea need te show yoer work cearly and esplain your reasoning in order to get credit. of a child The 125 points! Two women came before King Solomon, á puting who was the true moth Bible takes up the story in I Kings: Then the king said, "Bring me a sword" So they brought a sweed Sor the king. He then gave an order: "Cut the living child in two and give half to eee [woman) and halfso the other [woman]" The woman whose son was alive was filled with commpassion foe her soe and said to the king."Please, my loed give her the living baby Dehim!" But the other said, "Neither I noe you shall harve him. Cut him in two Then the king gave his ruling "Give the living baby to the first woman. Do not kill him; she is his mother a. 15 peints Grven that King Solomon does not initially know who the real mother is, and assuming that the king prefers the true mother to have the kid, and also that the true mother values the kid moee than the other 1) 1 peiats) Is this a principal-agent problem? If so, state and briefly explain whether it is an adverse clection or moral hazard problem, and identify thc principalls) and the aprms 2 11 psiats) According to the story, what kind of a strategy is King Solomon playing (signaling o 3) peiats Would the stralegy still work if the seoond woman had understiood what was poing on and simply repeatod whatever the first woma said b. 120 peints Consider a different version of this story in which now a game theory king is trying to persuade the two women sell the truth. Call the two women Anna and Bess. The king sets up the following pame Move 1: The king decides on a fine, F Move 2 Anna is asked to cither give up her claim, in which case Bess gots the child and the game ends (Anna gets zcro), ee to assert her claim, in which case we go on to Move 3 Move 3 Bess can cither accept Anna's claim, in which case Anna gets the child and the game ends (Bess gets zero) or challenge Anna's claim. In the later case, Bess ust put in a bod, B, oher own choosing for the cild and we go on to Move 4 Move 4 Anna can either match Bess's bid, in which case Anna gets the child and pays B to the king, while Bess pays the fine, F, to the king: or Anna docs not match, in which case Bess gets the child and pays har bid so the king, Anna pays the ne F Assume that the true mother values the child more than the false claimant. Denote the valuc of getting he child for Anna as vA and for Bess as v Note that the exact valucs are private information, that is, cach woman only knows her valuation; however, thcy both know that the true mother's valuation is greater than that of the falsue claimant. 1) 110 points Draw the game tree. Consider only the payefls to Anna and Bess Hint: Note that the fine, F, is defined as a (+) number so you need to use "-F while writing the payoffs 2) 110 points Consider the case in which Anna is the true mother, ie.VA>V and find the subpame perfect equilibrium. Hint: Since this is a sequential-move-game with perfect information, the SPE is equivalent to the Backward IRONUSI 15 points Consider the case in which Bess is the truc mother,ic. vand find the subgame-perfoct equilibrimExplanation / Answer
1) This story is one of the old example for applying theory to achieve and outcome .King solomen could not reach to a conculsion before testing the water and studying the behavior of the mothers. While passing such an order he wanted to understand which women had more love and care for the kid , because the real mother would have never asked the kind to hurt her kid just to prove herself right.
a) This example proves principle agent problem because solomon is the principal trying to play a baysian game thoery with the two mothers in order to identify there strategies ,his aim was to maximise the probability of choosing the right mother but the identity of these agents and there agendas are hidden from him .
b)In this game there is a lot of incomplete information causing a moral hazard problem ,second women knows the outcome and wants to hide the truth to earn reward .Therefore to find truth he created a situation for either parties to act upon this is process is called screening .
c)If the player is watching what the other players says or does that works to be a disadvantage , if one of them have special information they would try to concel it to their best interest. If actions of one become an advantage to other it becomes a form of signalling
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.