The police have apprehended two suspects for a crime. Since they don't have enough information to convict, they decide to extract a confession from them by putting each suspect in a separate room and offering them the following deal: "If you Confess and your partner doesn't, I can promise you a reduced (one-year) sentence, and on the basis of your confession, your partner will get 10 years. "If you both Confess, you will each get a three-year sentence." Each suspect also knows that if neither of them confesses, the lack of evidence will cause them to be tried for a lesser crime for which they will receive two-year sentences. A player strategy in this game would be for: these are all possible strategies stay silent if the other player stays silent confess no matter what the other player does confess if the other player confesses

The police have apprehended two suspects for a crime. Since they don't have enough information to convict, they decide to extract a confession from them by putting each suspect in a separate room and offering them the following deal: "If you Confess and your partner doesn't, I can promise you a reduced (one-year) sentence, and on the basis of your confession, your partner will get 10 years. "If you both Confess, you will each get a three-year sentence." Each suspect also knows that if neither of them confesses, the lack of evidence will cause them to be tried for a lesser crime for which they will receive two-year sentences. A player strategy in this game would be for: these are all possible strategies stay silent if the other player stays silent confess no matter what the other player does confess if the other player confesses

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.8P

See similar textbooks

Similar questions

Jane and Bill are apprehended for a bank robbery. They are taken into separate rooms and questioned by the police about their involvement in the crime. The police tell them each that if they confess and turn the other person in, they will receive a lighter sentence. If they both confess, they will each be sentenced to 30 years. If neither confesses, they will each receive a 20-year sentence. If only one confesses, the confessor will receive 15 years and the one who stayed silent will receive 35 years. The table below represents the choices available to Jane and Bill. If Jane trusts Bill to stay silent, what should she do? If Jane thinks that Bill will confess, what should she do? Does Jane have a dominant strategy? A = Confess; B = Stay Silent. (Each results entry lists Janes sentence first (in years), and Bill's sentence second.) A A (30,30) A B (35,15) B A (15, 35) B B (20, 20)
Suppose there are two groups -Wegofurst and Thenwego- who must make choices without knowing what the other has selected. Wegofurst, the player on the left, must choose A, B, or C. Thenwego, the player on the top must pick either X, Y, or Z. The outcomes described in the table below are desirable outcomes (such as profit in dollars, not years in prison): Thenwego Y 11,59 22,53 38, 24 Wegofurst B 35, 33 27 ,41 29, 37 C 28 , 36 39,23 47, 21 Assuming there is no collusion, what is the solution ? O There is NO correct solution listed. O AY OCY OcZ O BX O AX CX O AZ O BZ
Jane and Bill are apprehended for a bank robbery. They are taken into separate rooms and questioned by the police about their involvement in the crime. The police tell them each that if they confess and turn the other person in, they will receive a lighter sentence. If they both confess, they will be each be sentenced to 30 years. If neither confesses, they will each receive a 20-year sentence. If only one confesses, the confessor will receive 15 years and the one who stayed silent will receive 35 years. The table below represents the choices available to Jane and Bill. If Jane trusts Bill to stay silent, what should she do? A = Confess; B = Stay Silent (Each results entry lists Janes's sentence first (in years), and Bill's sentence second.) Jane A B Bill A (30, 30) (15, 35) B (35, 15) (20, 20)
Jane and Bill are apprehended for a bank robbery. They are taken into separate rooms and questioned by the police about their involvement in the crime. The police tell them each that if they confess and turn the other person in, they will receive a lighter sentence. If they both confess, they will be each be sentenced to 30 years. If neither confesses, they will each receive a 20-year sentence. If only one confesses, the confessor will receive 15 years and the one who stayed silent will receive 35 years. Table 10.7 below represents the choices available to Jane and Bill. If Jane trusts Bill to stay silent, what should she do? If Jane thinks that Bill will confess, what should she do? Does Jane have a dominant strategy? Does Bill have a dominant strategy? A = Confess; B = Stay Silent. (Each results entry lists Jane’s sentence first (in years), and Bill's sentence second.)
Jane and Bill are apprehended for a bank robbery. They are taken into separate rooms and questioned by the police about their involvement in the crime. The police tell them each that if they confess and turn the other person in, they will receive a lighter sentence. If they both confess, they will be each be sentenced to 30 years. If neither confesses, they will each receive a 20-year sentence. If only one confesses, the confessor will receive 15 years and the one who stayed silent will receive 35 years. The table below represents the choices available to Jane and Bill. Which criminal(s) have a dominate strategy to cheat? A = Confess; B = Stay Silent. (Each results entry lists Janes's sentence first (in years), and Bill's sentence second.) Jane A B Bill A (30, 30) (15, 35) B (35, 15) (20, 20) Question 3 options: Only Bill has a dominate strategy so he should cheat Only Jane has a dominate strategy so she should cheat Both Bill…
Jane and Bill are apprehended for a bank robbery. They are taken into separate rooms and questioned by the police about their involvement in the crime. The police tell them each that if they confess and turn the other person in, they will receive a lighter sentence. If they both confess, they will be each be sentenced to 30 years. If neither confesses, they will each receive a 20-year sentence. If only one confesses, the confessor will receive 15 years and the one who stayed silent will receive 35 years. Table 10.7 e below represents the choices available to Jane and Bill. A = Confess; B = Stay Silent. (Each results entry lists Bill's sentence fırst (in years), and Jane's sentence second). Answer the following: Jane A B A (30, 30) (15, 35) Bill (35, 15) (20, 20) Table 10.7 a) If Jane trusts Bill to stay silent, what should she do? b) If Jane thinks that Bill will confess, what should she do? c) Does Jane have a dominant strategy? Does Bill have a dominant strategy? Justify your answer.
Jane and Bill are apprehended for a bank robbery. They are taken into separate rooms and questioned by the police about their involvement in the crime. The police tell them each that if they confess and turn the other person in, they will receive a lighter sentence. If they both confess, they will be each be sentenced to 30 years. If neither confesses, they will each receive a 20-year sentence. If only one confesses, the confessor will receive 15 years and the one who stayed silent will receive 35 years. The table below represents the choices available to Jane and Bill. If Jane thinks that Bill will confess, what should she do? A = Confess; B = Stay Silent. (Each results entry lists Janes's sentence first (in years), and Bill's sentence second.)
While grading a final exam, an economics professordiscovers that two students have virtually identical answers.She is convinced the two cheated but cannot prove it. The professorspeaks with each student separately and offers the followingdeal: Sign a statement admitting to cheating. If both studentssign the statement, each will receive an “F” for the course. Ifonly one signs, he is allowed to withdraw from the course whilethe other student is expelled. If neither signs, both receive a “C”because the professor does not have sufficient evidence to provecheating.a. Draw the payoff matrix.b. Which outcome do you expect? Why?
While grading a final exam a professor discovers that two students have virtually identical answers. She talks to each student separately and tells them that she is sure that they shared answers, but she cannot be sure who copied from whom. She offers each student a deal-if they both sign a statement admitting to the cheating, each will be given an F for the course. If only one signs the statement, that student will be allowed to withdraw from the course and the other nonsigning student will be expelled from the university. Finally, if neither signs the statement they will both get a C for the course because the professor does not have enough evidence to prove that cheating has occurred. Assuming the students are not allowed to communicate with one another, set up the relevant payoff matrix. Beth doesn't sign Beth signs Beth: (Click to select) v Bob: (Click to select) v Beth: (Click to select) Bob: (Click to select) v Bob signs Beth: (Click to select) v Bob doesn't sign Bob: (Click to…
Does each individual in a prisoners dilemma benefit more from cooperation or from pursuing self-interest? Explain briefly.
A game theory problem: Two lawyers, Elizabeth Hasenpeffer (EH) and Joseph Fargillio (JF) decide on one of two legal strategies: A and B for EH, / and // for JF. They then write a brief and submit them simultaneously to three judges (X, Y, and Z) Suppose, at the start of the game, it is known by all that Judge Z will read only the brief of Ms. Hasenpeffer. Required: Write down the corresponding extensive form game. You may exclude payoffs.
1) Define Cartel and give an example. 2) Thelma and Louise are being charged for a murder/robbery. They are separated by police and interrogated. They are given the choice to confess or not to confess. The payoff matrix below identifies the years that they will each spend in jail, for the various outcomes. Louise Confess Don't Confess Confess (2 10,10 15.2 Thelma Don't Confess 2,15 3,3 a. Identify the Dominant Strategy for either player, or state that there isn't one. Remember, a "Strategy" is the players move. In this example, state "Confess" or "Don't Confess" for each player, not the payoff. b. Identify the Nash Equilibrium.