Use the following setting for questions 1-3. Consider the following static game: CR L 3,1 0,0 5,0 T M 2,1 1,2 3,1 B 1,2 0,1 4,4 Suppose this game is played for two periods. At the beginning of period 2, the players can observe the outcome from period 1. There is no discounting. 1. First, assume only pure-strategy SPNE such that either player's second period strategy DOES NOT depend on the first period outcome. How many such SPNE are in this game? (a) 1 (b) 2 (c) 3 (d) 4 (e) none

Use the following setting for questions 1-3. Consider the following static game: CR L 3,1 0,0 5,0 T M 2,1 1,2 3,1 B 1,2 0,1 4,4 Suppose this game is played for two periods. At the beginning of period 2, the players can observe the outcome from period 1. There is no discounting. 1. First, assume only pure-strategy SPNE such that either player's second period strategy DOES NOT depend on the first period outcome. How many such SPNE are in this game? (a) 1 (b) 2 (c) 3 (d) 4 (e) none

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.9P

See similar textbooks

Similar questions

Consider the following coordination game: Player 2P1 Comedy Show Concert Comedy Show 11,5 0,0 Concert 0,0 2,2 a. Find the Nash equilibrium(s) for this game.b. Now assume Player 1 and Player 2 have distributional preferences. Specifically, both people greatly care about the utility of the other person. In fact, they place equal weight on their outcome and the other person’soutcome, ρ = σ = ½. Find the Nash equilibrium(s) with these utilitarianpreferences.c. Now consider the case where Player1 and Player2 do not like each other. Specifically, any positive outcome for the other person is viewed as anegative outcome for the individual, ρ = σ = -1. Find the Nashequilibrium(s) with these envious preferences.
Find all NE of the stage game.(b) Consider a two-period game without discounting in which the stage game is played ineach period. Find all pure strategy SPNE.(c) What’s the min-max payoff of each player?(c1) Consider pure strategies only.(c2) Consider all strategies, including the mixed ones.(d) Now suppose the stage game is repeated infinitely many times. Use the Fudenberg-Maskin Folk theorem to find all possible values of payoff that can be supported as aSPNE.
Consider the game with the payoffs below. Which of the possible outcomes are MORE efficient than the Nash Equilibrium (NE)? Note, they do NOT need to be Nash equilibria themselves, they just need to be more efficient than the NE. Multiple answers are possible, but not necessary. You need to check ALL correct answers for full credit. JILL High Medium LowMAGGIE Left 3,4 2,3 2,2Center 4,8 9,7 8,7Right 7,6 8,5 9,4Group of answer choices (Left, Low) There is no strategy combination that is more efficient than the Nash equilibrium for this game. (Right, Medium) (Left, High) (Center, Medium) (Center, High) (Center, Low) (Left, Medium) (Right, Low) (Right, High)
Consider the location game we covered in Lecture 3. Now assume there arethree players (vendors). As we assumed in the lecture, consumers in each area choosethe closest vendor and if there are multiple closest vendors then these vendors receiveequal share of consumers in the area. Notice Si = {1, 2, 3, ...., 9} for i = 1, 2, 3. Here aresome examples of payoffs: u1(1, 1, 1) = 3, u1(1, 1, 9) = u2(1, 1, 9) = 2.25, u3(1, 1, 9) =4.5, u1(1, 5, 9) = u3(1, 5, 9) = 2.5 and u2(1, 5, 9) = 4. (a) Is s′1 = 1 strictly dominated by s′′1 = 2 for player 1?(b) Is s′1 = 1 weakly dominated by s′′1 = 2 for player 1?(c) Can you find a Nash equilibrium in pure strategies?
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?
We’ll now show how a college degree can get you a better job even if itdoesn’t make you a better worker. Consider a two-player game between aprospective employee, whom we’ll refer to as the applicant, and an employer. The applicant’s type is her intellect, which may be low, moderate,or high, with probability 1/3 , 1/2 , and 1/6 , respectively. After the applicantlearns her type, she decides whether or not to go to college. The personalcost in gaining a college degree is higher when the applicant is less intelligent, because a less smart student has to work harder if she is to graduate. Assume that the cost of gaining a college degree is 2, 4, and 6 for an applicant who is of high, moderate, and low intelligence, respectively.The employer decides whether to offer the applicant a job as a manageror as a clerk. The applicant’s payoff to being hired as a manager is 15,while the payoff to being a clerk is 10. These payoffs are independent ofthe applicant’s type. The employer’s payoff from…
(a) Calculate the safety levels of both players.(b) Find the set of all Nash equilibria (pure and mixed).
Consider Bernard \ Mary Left Center Right Top 0,5 1,0 2,2 Bottom 1,0 0,3 2,2 The first number in a cell denotes the payoff to Bernard and the second number denotes the payoff to MaryForexample: πB(B,L)=1and πM(T,L)=5. a Give all pure strategy Nash equilibria of this one-shot game, if any. Briefly explain.Let Bernard play Top with probability p and Bottom with probability 1 − p; let Mary play Left with probability qL , Center with probability qC and Right with probability qR = 1 − qL − qC . b Give all mixed strategy Nash equilibria of this game.
** 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 the following variation to the Rock (R), Paper (P), Scissors (S) game:• Suppose that the Player 1 (row player) has a single type, Normal.• Player 2 (column player) has two types Normal and Simple.• A player of Normal type plays this zero-sum game as we studied in class whereas a player of type Simple always play P.• Player 2 knows whether he is Normal or Simple, but player 1does not.a) Suppose player 2 is of type Normal with probability 1/3 and of type Simple with probability (2/3). Find all pure strategy Bayesian Nash Equilibria.b) Suppose player 2 is of type Normal with probability 2/3 and of type Simple with probability (1/3). Find all pure strategy Bayesian Nash Equilibria.
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.
You and a rival are engaged in a game in which there are three possible outcomes: you win, your rival wins (you lose), or the two of you tie. You get a payoff of 50 if you win, a payoff of 20 if you tie, and a payoff of 0 if you lose. What is your expected payoff in each of the following situations? (a) There is a 50% chance that the game ends in a tie, but only a 10% chance that you win. (There is thus a 40% chance that you lose.) (b) There is a 50–50 chance that you win or lose. There are no ties. (c) There is an 80% chance that you lose, a 10% chance that you win, and a 10% chance that you tie.