For the first six questions, consider Joe and Sally, two fourth-graders who have been caught in the school library breaking two major rules: chewing gum and reading comic books when they are supposed to be reading a class assignment. Both offenses are punished in terms of days of after-school detention. In the case of gum, all students found chewing it are punished the same, regardless of who brought the gum to school, and it’s quite easy to find out who’s chewing it. In the case of comic books, however, the student(s) who supply comic books for others are punished much more harshly than the students who are simply reading them.So the school principal, eager to look good at identifying and taking care of student problems due to a workplace evaluation coming up soon, pulls Joe and Sally aside separately. She tells each of them that if he/she will confess to bringing the comic books, he/she will receive a much smaller punishment (fewer days of detention). If both or neither confess, the number of days of detention will differ as described by the attached game in tree format. On that tree, C means to confess, and N means not to confess, while J and S are the first initials of each player. Everything else is the same as in the PowerPoints.Using the information on the tree, which of the following is true? ( The tree is attached)1.)A. If only Joe confesses, Sally will receive 1 day of detention.B. If only Sally confesses, Joe will receive 3 days of detention.C. If both Joe and Sally confess, Sally will receive 3 days of detention.D. If neither Joe nor Sally confesses, Joe will receive 6 days of detention.2.Continue working with the attached table portraying the game with Joe and Sally. Which of the following best describes Sally’s dominant strategy in this game?A. confessing, but only if Joe does not confessB. confessing, no matter what Joe doesC. not confessing, but only if Joe confessesD. not confessing, no matter what Joe does3.Keep using the attached game in tree format concerning Joe and Sally.The Nash equilibrium in this situation can be best described asA. there is no Nash equilibriumB. there is more than one Nash equilibriumC. (Joe: confess, Sally: don’t confess)D. (Joe: don’t confess, Sally: confess)E. (Joe: confess, Sally: confess)F. (Joe: don’t confess, Sally: don’t confess)4.Keep using the attached game in tree format concerning Joe and Sally.Which of the following is true about this game’s Nash equilibrium?A. It is stable.B. It is not stable.C. There is no Nash equilibrium.D. None of the above.5.Keep using the attached game in tree format concerning Joe and Sally.If you found a Nash equilibrium for the game, is there any choice Joe and Sally could agree to make that would make them both better off than the Nash equilibrium outcome? If so, what is it?A. Yes; they could agree for one to confess and the other not to.B. No; the Nash equilibrium is the best possible choice for both.C. Yes; they could agree for both not to confess.D. None of the above – there is no Nash equilibrium.6.Keep using the attached game in tree format concerning Joe and Sally.If you found that Joe and Sally could do better by making an agreement different from the Nash equilibrium, what is most likely to happen after this agreement is made?A. If Joe is the one who brought the comics, he is most likely to renege on the agreement.B. If Joe is the one who brought the comics, Sally is most likely to renege on the agreement.C. Neither will likely renege on the agreement.D. Both will likely renege on the agreement.E. None of the above – there is no Nash equilibrium, or there is no agreement that would make them better off than the Nash equilibrium.7.For the next four questions, consider the game in tabular format attached to this question. It depicts a game between Firms X and Y in which each is deciding between two particular pricing structures (1 or 2); the payoffs depict their estimated total profits in millions for each choice, so that for example a payoff of 99 would mean estimated profits of $99 million. Use all the same assumptions as in our practice problems.The Nash equilibrium for this game would be:A. X:1, Y:2B. X:2, Y:2C. X:1, Y:1D. X:2, Y:1E. None of the above, or there is no Nash equilibrium.8.This question has not been answered completelyContinue to consider the same game as in the previous question.Which of the following is true about this game?A. It is similar to the Prisoner’s Dilemma in that both players could do better if they colluded compared to the Nash equilibrium.B. It is not similar to the Prisoner’s Dilemma in that neither player could do better than the Nash equilibrium.C. It is not similar to the Prisoner’s Dilemma because only one player could do better than the Nash equilibirum.D. It is similar to the Prisoner’s Dilemma because there is no Nash equilibrium.E. None of the above is true, or we don’t have enough information to answer the question.9.Note the special directions for this question:Continue to consider the game from the previous question. If both firms started out with estimated profits of $20 million, the Nash equilibrium would result in a ______ increase/decrease in estimated profits for Firm Y.Enter your number in millions of dollars. For example, if you want to enter $99 million ($99,000,000) enter 99 in the blank. Enter your answer as a whole number; include a negative sign for a decrease in estimated profits and no sign for an increase in estimated profits._________________10.Note the special directions for this question:Continue to consider the game from the previous question. In the Nash Equilibrium (if any), Firm X would have estimated profits of $_______ million. If there is no Nash Equilibrium, enter 11111 in the blank.Enter your answer in millions of dollars. For example, if you want to enter $99 million ($99,000,000) enter 99 in the blank. Enter only numbers.
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