up Thu 7:05 PM P. O Presentation EB 75% Tasks 12-14 2020.pdf (page 2 of 2) - Q Search uenaa 2. Find all Nash equilibria in the following game. The first entry in each cell is the payoff to player 1, the second entry is the one to player 2. Is there a dominant strategy for any player? Predict the outcome of this game. player 2 left right player 1 up 5,1 1,0 bottom 3,1 2,2 3. Consider the game in the preceding strategic form. Suppose player 1 moves first and player 2 moves after observing player 1's choice. Find the extensive form of this game and solve it by backward induction. Predict the outcome of this prediction to the one you made for the simultaneous version of this game. game and compare your 4. Find all Nash equilibria in the following game. The first entry in each cell is the payoff to player 1, the second entry is the one to player 2. Is there a dominant strategy for any player? Predict the outcome of this game. player 2 left right 5,1 bottom 8,2 player 1 up 1,0 2,1 5. Find all Nash equilibria in the following game. The first entry in each cell is the payoff to player 1, the second entry is the one to player 2. player 2 left middle right player 1 6,2 dn 4,1 5,24 MacBook Air

up Thu 7:05 PM P. O Presentation EB 75% Tasks 12-14 2020.pdf (page 2 of 2) - Q Search uenaa 2. Find all Nash equilibria in the following game. The first entry in each cell is the payoff to player 1, the second entry is the one to player 2. Is there a dominant strategy for any player? Predict the outcome of this game. player 2 left right player 1 up 5,1 1,0 bottom 3,1 2,2 3. Consider the game in the preceding strategic form. Suppose player 1 moves first and player 2 moves after observing player 1's choice. Find the extensive form of this game and solve it by backward induction. Predict the outcome of this prediction to the one you made for the simultaneous version of this game. game and compare your 4. Find all Nash equilibria in the following game. The first entry in each cell is the payoff to player 1, the second entry is the one to player 2. Is there a dominant strategy for any player? Predict the outcome of this game. player 2 left right 5,1 bottom 8,2 player 1 up 1,0 2,1 5. Find all Nash equilibria in the following game. The first entry in each cell is the payoff to player 1, the second entry is the one to player 2. player 2 left middle right player 1 6,2 dn 4,1 5,24 MacBook Air

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.3P

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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.
1) What are the Nash equilibria? Which one is unreasonable/non-credible threat? 2) What are the subgame perfect Nash equilibria? Does SPNE concept eliminate the unreasonable Nash equilibrium?
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?
12. Consider a game where each player picks a number from 0 to 60. The guess that is closest to half ofthe average of the chosen numbers wins a prize. If several peopleare equally close, then they share theprize. The game theory implies that (A) all players have dominant strategies to choose 0 (B) all players have dominant strategies to choose 30 (C) there is a Nash equilibrium where all players pick 0 (D) there is a Nash equilibrium where all players pick positive numbers 13. Behavioral data in such games suggests that (A) most subjects choose 0; (B) most subjects choose 30; (C) common answers include 30, 15, 7.5, and 0; (D) most subjects use randomization. Can you help me answer number 13 please?
What is Ann's maximin strategy? Game Bob L RAnn U 10,-1 4, 4 D 4, 1 8, -1 Select one: a.none of the other answers b.4/7 U + 3/7 D c.2/5 U+ 3/5 D d.2/7 U + 5/7 D e.3/5 U + 2/5 D
a Suppose you are given a choice between thefollowing options:A1: Win $30 for sureA2: 80% chance of winning $45 and 20% chance ofA2: winning nothing B1: 25% chance of winning $30B2: 20% chance of winning $45Most people prefer A1 to A2 and B2 to B1. Explainwhy this behavior violates the assumption that decisionmakers maximize expected utility.b Now suppose you play the following game: You havea 75% chance of winning nothing and a 25% chance ofplaying the second stage of the game. If you reach thesecond stage, you have a choice of two options (C1 andC2), but your choice must be made now, before youreach the second stage.C1: Win $30 for sureC2: 80% chance of winning $45 13.5 Bayes’ Rule and Decision Trees 767Most people choose C1 over C2 and B2 to B1 (from part(a)). Explain why this again violates the assumption ofexpected utility maximization. Tversky and Kahneman(1981) speculate that most people are attracted to thesure $30 in the second stage, even though the secondstage may never be…
Consider the payoff matrix for a game depicted below. Player 1 selects the row and Player 2 selects the column. Up Down Left 1, -1 -1, 1 Right -1, 1 1, -1 What is (are) the Nash equilibrium (equilibria)? Question 18Answer a. Player 1 plays right; Player 2 plays down b. Player 1 plays left; Player 2 plays down c. Player 1 plays down; Player 2 plays left d. Player 1 plays right; Player 2 plays up e. Player 1 plays up; Player 2 plays left f. There is no Nash equilibrium g. Player 1 plays down; Player 2 plays right h. Player 1 plays up; Player 2 plays right i. Player 1 plays left; Player 2 plays up
Bob is playing 1/4 L + 3/4 R. What is Ann's expected payoff of playing D? Game Bob L RAnn U 10,-1 0, 1 D 4, 1 8, -1
H2. One day, Sam and Ryan play odds/evens to see who gets the last doughnut. On command, they each extend one or two fingers. If the sum is odd Sam wins the doughnut, if the sum is even Ryan wins the doughnut. Suppose the payoff from winning the doughnut is 1 and the payoff from losing is 0. a) Illustrate this interaction as a game in matrix form. b) Suppose that Sam thinks that Ryan will play one finger for sure? What will Sam play? Does Sam have reason to think that Ryan will play one finger for sure? c) Do either of them have a strictly dominated strategy? d) Find the pure strategy Nash equilibria of the game, if any. e) Suppose that Sam thinks that Ryan will play one finger or two fingers with even odds. Will Ryan play one finger for sure, play two fingers for sure or play each strategy with even odds? Does Sam have good reason to believe that Ryan will play one finger or two fingers with even odds?
. Find the Nash equilibrium of the following modified Rock-Paper-Scissors game: • When rock (R) beats scissors (S), the winner’s payoff is 10 and the loser’s payoff is −10. • When paper (P) beats rock, the winner’s payoff is 5 and the loser’s payoff is −5. • When scissors beats paper, the winner’s payoff is 2 and the loser’s payoff is −2. • In case of ties, both players receive 0 payoff. You are suposed to create a system of equations and then solve for them and find 3 probabilities- please show how to do that
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 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.