Two players, Row and Column, will simultaneously and independently decide whether to 'share' or 'steal'. Cash outcomes have a 'prisoner's dilemma' structure. However, Column feels shame s > 0 if they choose 'Steal'. Row's payoff is their cash outcome; Column's is their cash outcome, minus their shame if they 'Steal'. The following matrix summarizes (each cell has Row's payoff first, and Column's second): Column Share Steal 0,8 – s 2, 2 – s Share 5,5 8,0 Row Steal This game has a unique Nash equilibrium, but it depends on s. What is the Nash equilibrium of this game, for different values of s? Explain.

Two players, Row and Column, will simultaneously and independently decide whether to 'share' or 'steal'. Cash outcomes have a 'prisoner's dilemma' structure. However, Column feels shame s > 0 if they choose 'Steal'. Row's payoff is their cash outcome; Column's is their cash outcome, minus their shame if they 'Steal'. The following matrix summarizes (each cell has Row's payoff first, and Column's second): Column Share Steal 0,8 – s 2, 2 – s Share 5,5 8,0 Row Steal This game has a unique Nash equilibrium, but it depends on s. What is the Nash equilibrium of this game, for different values of s? Explain.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.2P

See similar textbooks

Similar questions

Consider the following game where two players have to decide if they want to buy a movie ticket or a baseball ticket. They have the highest payoffs when they both buy tickets to the same activity, but must decide simultaneously what to buy without knowing what the other person will do. a. Does either player have a dominant strategy? b. How many equilibria does this game have? c. Is this an example of a prisoner’s dilemma? Explain. d. What will be the outcome if your friend buys their ticket first and you can observe their choice?
Consider the game shown below. In this game, players 1 and 2 must move at the same time without knowledge of the other player’s move. Player 1’s choices are shown in the row headings (A/B), Player 2’s choices are shown in the column headings (C/D). The first payoff is for the row player (Player1) and the second payoff is for the column player (Player 2). Player 2 Player 1 C D A 8, 3 2, 4 B 7, 4 3, 5 Pick the correct answer: Player 1: Has a dominant strategy to choose A Has a dominant strategy to choose B Has a dominant strategy to choose C Has a dominant strategy to choose D Does not have a dominant strategy Player 2: Has a dominant strategy to choose A Has a dominant strategy to choose B Has a dominant strategy to choose C Has a dominant strategy to choose D Does not have a dominant strategy The Nash equilibrium outcome to this game is: A/C A/D B/C B/D There is no pure strategy Nash equilibrium for this game
Consider the game the following game: - Two players, six rounds of decision-making alternating between player 1 and 2, starting with player 1. - Game starts with $0.50. The player making the decision is given the option to Grab (80% of the money), or Leave it to double in the next round. - If player 2 picks Leave in the last round, she receives $6.40, and player 1 receives $25.60. Solve game via Backwards Induction.
In the collusion game, we found that collusion was only sustainable in the infinite horizon repeated game. One Nash Equilbrium of that game can be found when all players play a “grim trigger” strategy, where they collude until an opponent chooses to compete, and then compete for all future rounds as a punishment. In such a game, if the one period bonus that comes from competing is low enough, firms always collude and the punishment is never triggered. However, let’s think a little deeper about this Nash Equilibrium. Is the punishment (vowing to compete forever after one deviates) realistic, especially if firms can communicate freely? Why or why not? (Hint: Is a grim trigger Nash Equilibrium a Subgame Perfect Nash Equilibrium? What kinds of Nash Equilibria does Subgame Perfection rule out in sequential games?)
(A) Two California teenagers Bill and Ted are playing Chicken. Bill drives his hot rod south down a one-lane road, and Ted drives his hot rod north along the same road. Each has two strategies: Stay or Swerve. If one player chooses Swerve he loses face; if both swerve, they both lose face. However, if they both choose Stay, they are both killed. The payoffs for the game of Chicken are given in the table below. Bill is the row player and Ted is the column player. Stay Swerve Stay -3, -3 2, 0 Swerve 0, 2 1, 1 (i) Find all pure strategy Nash equilibria. (ii) Find the mixed strategy Nash equilibrium. (iii) What is the probability that both teenagers will survive? Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.
The game of Chicken is played by two teens who speed toward each other on a single-lane road. The first to veer off is branded the chicken, whereas the one who does not veer gains peer-group esteem. Of course, if neither veers, both die in the resulting crash. Payoffs to the Chicken game are provided in the following table. Team 2 Veer Does not veer Team 1 Veer 2, 2 1, 3 Does not veer 3, 1 0, 0 The first payoff number is for Teen 1 and the second number is for Teen 2. a) Does any of the players has a dominant strategy? b) Find the pure-strategy Nash equilibrium or equilibria. c) Suppose the game is played sequentially. Find the Nash equilibrium.
Use the following payoff matrix for a one-shot game to answer the accompanying questions. a. Determine the Nash equilibrium outcomes that arise if the players make decisions independently, simultaneously, and without any communication. Which of these outcomes would you consider most likely? Explain. b. Suppose player 1 is permitted to “communicate” by uttering one syllable before the players simultaneously and independently make their decisions. What should player 1 utter, and what outcome do you think would occur as a result? c. Suppose player 2 can choose its strategy before player 1, that player 1 observes player 2’s choice before making her decision, and that this move structure is known by both players. What outcome would you expect? Explain.
Consider the game shown below. In this game, players 1 and 2 must move at the same time without knowledge of the other player’s move. Player 1’s choices are shown in the row headings (A, B, C, D), Player 2’s choices are shown in the column headings (E, F, G). The first payoff is for the row player (Player 1) and the second payoff is for the column player (Player 2). Player 2 Player 1 E F G A 2, 4 7, 7 2, 6 B 10, 6 1, 7 12, 4 C 4, 6 8, 8 7, 7 D 1, 6 3, 9 6, 7
True or False? Explain in 2-3 sentences. If both players use grim trigger strategies, they could (depending on the value of 5) sustain cooperation as a subgame-perfect Nash equilibrium outcome in a finitely repeated prisoners' dilemma. Please do fast.. ASAP fast
Consider the game shown below. In this game, players 1 and 2 must move at the same time without knowledge of the other player’s move. Player 1’s choices are shown in the row headings (A, B, C, D), Player 2’s choices are shown in the column headings (E, F, G). The first payoff is for the row player (Player1) and the second payoff is for the column player (Player 2). Player 2 Player 1 E F G A 2, 7 7, 2 2, 6 B 5, 5 5, 4 8, 4 C 4, 6 8, 4 7, 5 D 1, 6 3, 5 6, 4 Highlight the correct answer: Player 1: Has a dominant strategy to choose A Has a dominant strategy to choose B Has a dominant strategy to choose C Has a dominant strategy to choose D Does not have a dominant strategy Player 2: Has a dominant strategy to choose E Has a dominant strategy to choose F Has a dominant strategy to choose G Does not have a dominant strategy The Nash equilibrium outcome to this game is: A/F B/E B/G C/F C/G There is no pure strategy Nash…
Untied and Air ’R’ Us are the only two airlines operating flights between Collegeville and Bigtown. Each airline can charge either a high price or a low price for a ticket. The accompanying matrix shows their payoffs, in profits per seat (in dollars), for any choice that the two airlines can make. Suppose the two airlines play a one-shot game—that is, they interact only once and never again. What will be the Nash (noncooperative) equilibrium in this one-shot game? Explain why this is the likely outcome. Now suppose the two airlines play this game twice. Each airline then considers the future and decides on a “tit-for-tat” strategy, that is, it starts off charging the high price in the first period, and then in the second period it does whatever the other airline did in the previous period. If both play this…
Consider the following two person game. Player 1 begins the game by choosing A or B. If Player 1 chooses A the game ends and Player 1 receives $100 and Player 2 receives $100. If Player 1 chooses B then Player 2 must choose C or D. If Player 2 chooses C then Player 1 receives $150 and Player 2 receives $250. If Player 2 chooses D then Player 1 receives $0 and Player 2 receives $400. Draw the complete game tree for this situation. Be sure to accurately label the tree and include the payoffs. Using backwards induction (look forward and reason backwards) determine the rational outcome to this game. Given how experimental subjects have behaved in the Ultimatum game, provide a behavioral explanation for why an “average” Player 1 and 2 might deviate from the rational prediction.