(Game Theory) While grading a final exam, an econom- ics professor discovers that two students have virtually identical answers. She is convinced the two cheated but cannot prove it. The professor speaks with each student separately and offers the following deal: Sign a statement admitting to cheating. If both students sign the statement, each will receive an “F" for the course. If only one signs, he is allowed to withdraw from the cours- while the other student is expelled. If neither signs, both receive a "C" because the professor does not have suf- ficient evidence to prove cheating. a. Draw the payoff matrix. b. Which outcome do you expect? Why?

(Game Theory) While grading a final exam, an econom- ics professor discovers that two students have virtually identical answers. She is convinced the two cheated but cannot prove it. The professor speaks with each student separately and offers the following deal: Sign a statement admitting to cheating. If both students sign the statement, each will receive an “F" for the course. If only one signs, he is allowed to withdraw from the cours- while the other student is expelled. If neither signs, both receive a "C" because the professor does not have suf- ficient evidence to prove cheating. a. Draw the payoff matrix. b. Which outcome do you expect? Why?

Principles of Economics (MindTap Course List)

8th Edition

ISBN:9781305585126

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter17: Oligopoly

Section: Chapter Questions

Problem 5CQQ

See similar textbooks

Similar questions

A game is played as follows: First Player 1 decides (Y or N) whether or not to play.If she chooses N, the game ends. If she chooses Y, then Player 2 decides (Y or N) whetheror not to play. If he chooses N the game ends. If he chooses Y, then they go ahead and playanother game with the payoffs shown below. A player who opts out by choosing N gets 2 andthe other player gets 0. Draw the tree of this game and then find the two subgame-perfect Nashequilibria.
8. Two states, A and B, have signed an arms-control agreement. This agreementcommits them to refrain from building certain types of weapons. The agreement is supposed tohold for an indefinite length of time. However, A and B remain potential enemies who wouldprefer to be able to cheat and build more weapons than the other. The payoff table for A (player1, the row player) and B (player 2, the column player) in each period after signing thisagreement is below. a) First assume that each state uses Tit-for-Tat (TFT) as a strategy in this repeated game.The rate of return is r. For what values of r would it be worth it for player A to cheat bybuilding additional weapons just once against TFT? b) For what values of r would it be worth deviating from the agreement forever to buildweapons? c) Convert both values you found in parts a and b to the equivalent discount factor dusing the formula given in lecture and section. d) Use the answers you find to discuss the relationship between d and r:…
answer the ff: Suppose that each company cancharge either a high price for tickets or a low price. Ifone company charges $300, it earns low profit if theother company also charges $300 and high profit ifthe other company charges $600. On the other hand,if the company charges $600, it earns very low profit ifthe other company charges $300 and medium profitif the other company also charges $600.a. Draw the decision box for this game.b. What is the Nash equilibrium in this game?Explain.c. Is there an outcome that would be better than theNash equilibrium for both airlines? How could itbe achieved? Who would lose if it were achieved?
Required a. Identify three Nash equilibria of this game. b. Explain in words which strategy pair is likely to be played in this game and why. Please give a detailed answer. Thanks!
6 Two people will select a policy that affects both of them by applying a "veto" in a sequential and alternate manner, that is: person 1 begins to veto a policy and then person 2 exercises his "veto" with the remaining policies; the process repeats until only one policy remains. Assume that there are 3 policies: X,Y,Z, and that person 1 prefers X to Y to Z and person 2 prefers Z to Y to X. a. Represents the game extensively b. Give the number of subgames C. Indicate the total strategies of the players d. find all subgame perfect nash equilibria e. Find all Nash Equilibriums.
Game Theory a) Consider the following game represented by the game tree below. If you observe Blue Bank playing medium and Green Bank playing bottom, would you be surprised by their choices? Carefully explain why or why not. b) Now assume that Blue and Green Banks play the game with the same actions and payoffs as in a) but they make their choices simultaneously. What is the payoff matrix for this new game? What do you predict will happen in the game? Explain. c) Assume that the game from part a) is played five times, i.e. Blue and Green Banks play a repeated game with the stage game described in a). What do you predict will happen in the game? Explain.
Consider the extensive form game portrayed below. The top number at aterminal node is player 1’s payoff, the middle number is player 2’s payoff,and the bottom number is player 3’s payoff.a. Derive the strategy set for each player. (Note: If you do not want to listall of the strategies, you can provide a general description of a player’sstrategy, give an example, and state how many strategies are in thestrategy set.)b. Derive all subgame perfect Nash equilibria. c. Derive a Nash equilibrium that is not a SPNE, and explain why it isnot a SPNE.
** Please be advsed that this is practice only from previous yeasr *** Answers: (a) There are no Nash equilibria.(b) There are two pure strategy Nash equilibra, one with (H,H) and another with (L,L), and no mixed strategy Nash equilibria.(c) There are two pure strategy Nash equilibra, one with (H,H) and another with (L,L), and one mixed strategy Nash equilibria with p = 1/2 and q = 1/2.(d) There are two pure strategy Nash equilibra, one with (H,H) and another with (L,L), and one mixed strategy Nash equilibria with p = 1/2 and q = 3/4.(e) There are two pure strategy Nash equilibra, one with (H,H) and another with (L,L), and one mixed strategy Nash equilibria with p = 3/4 and q = 1/2.
Consider this extensive form game. The top number is player 1’s payoff, themiddle number is player 2’s payoff, and the bottom number is player 3’spayoff.a. Describe the general form of a strategy for each player.b. Find the SPNE.
(a) What are the sets of pure strategies of players A and B?(b) Find the subgame perfect equilibrium(c) Provide a brief argument why the SPE is unique (i.e., why there are no more SPE, whether in pure or mixed strategies).
Consider the following price game: Firm 1 Firm 2 High Low High 20, 20 12, 24 Low 24, 12 14, 14 Remark: In simultaneous move games (games with rows and columns) theconvention is to write the row player’s payoff first and the column player’spayoff second. (a) What is the Nash equilibrium of this game? Recall that for each playeryou should find the best response to each of the opponents’ strategies andunderline the associated payoff. Then look for a cell where both strategiesare best responses to each other. This is a Nash equilibrium. (b) Does either firm have a dominate strategy (a strategy that is always abest response)?
(a) Calculate the safety levels of both players.(b) Find the set of all Nash equilibria (pure and mixed).