Question 2 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 doesn't 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. TEEN 2 TEEN 1 Veer Don't Veer 2,2 3,1 Veer 1,3 0,0 Don't Veer a) Draw the extensive form. b) Find the pure-strategy Nash equilibrium or equilibria. c) Compute the mixed-strategy Nash equilibrium. As part of your answer draw the best- response function diagram for the mixed strategies. d) Suppose the game is played sequentially with teen A moving first and committing to this action by throwing away the steering wheel. What are teen B's contingent strategies? Write down the normal and extensive forms for the sequential version of the game. e) Using the normal form for the sequential version of the game, solve for the Nash equilibria. f) Identify the proper sub games in the extensive form for the sequential version of the game. Use backward induction to solve for the sub game-perfect equilibrium. Explain

Question 2 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 doesn't 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. TEEN 2 TEEN 1 Veer Don't Veer 2,2 3,1 Veer 1,3 0,0 Don't Veer a) Draw the extensive form. b) Find the pure-strategy Nash equilibrium or equilibria. c) Compute the mixed-strategy Nash equilibrium. As part of your answer draw the best- response function diagram for the mixed strategies. d) Suppose the game is played sequentially with teen A moving first and committing to this action by throwing away the steering wheel. What are teen B's contingent strategies? Write down the normal and extensive forms for the sequential version of the game. e) Using the normal form for the sequential version of the game, solve for the Nash equilibria. f) Identify the proper sub games in the extensive form for the sequential version of the game. Use backward induction to solve for the sub game-perfect equilibrium. Explain

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

5. A game of Chicken is played by two lorry drivers who speed toward a narrow bridge. If one driver stops to let the other pass, they waste time, whereas the one who does not stop gets to their destination quicker. However, if both keep driving straight on then they crash. The game is played once, and drivers move simultaneously. Payoffs are given below (assume 0 < x < 10): Drive Stop Drive -10,-10 -x, 8 Stop 8,-1 0,0 (a) Find any pure strategy Nash equilibria of this game. (b) Find the mixed strategy Nash equilibrium of this game. (c) What happens to the column player's equilibrium mixed strategy as x increases? Explain why this happens. (d) Let x = 1. What are the rationalizable outcomes of this game? Do these offer a better prediction than the Nash equilibria?
3. The following is an interpretation of the rivalry between the United States (USA) and the Soviet Ünion (USSR) during the cold war. Each side has the choice of two strategies: Aggressive and Restrained. The payoff table is given as follows: USSR Restrained Aggressiveness Restrained 4,3 1,4 USA Aggressiveness 3,1 2,2 a) Consider this game when the two countries move simultaneously. Find all pure strategy Nash equilibria. b) Next consider three alternative ways in which the game could be played with sequential moves: (i) The USA moves first and the USSR moves second. (i) the USSR moves first and the USA moves second. (i) The USSR moves first, and the USA moves second, but the USSR has a further move after the USA moves. For each case, draw the game tree and find the subgame-perfect Nash equilibrium. c) What are the key strategic issues (commitment, credibility and so on) for the two countries. (Note: Be concise. Your answer should not exceed 300 words].
38. Consider the following game. There are ten churches in town: nine are Catholic and one is Eastern Orthodox. All churches conduct their divine services at 10am on Sunday morning. You and your friend, without communication, agree to meet at a church service. If you fail to meet at the same church, then you are sad and become a Doomer. What is this game's focal point? Remember that you cannot communicate about this. (A) You meet at any of the Catholic churches. (B) You meet at any of the churches – denomination does not matter. We're all the same bro. (C) You meet at the Orthodox church. (D) There is no focal point. 39. Consider a fractional-reserve banking system in which an initial deposit of $1,000 can generate up to $4,000 in money. What is the reserve ratio? (A) 4 percent. (B) 5 percent. (C) 25 percent. (D) 75 percent.
7. Solving for dominant strategies and the Nash equilibrium Suppose Carlos and Deborah are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Carlos chooses Right and Deborah chooses Right, Carlos will receive a payoff of 5 and Deborah will receive a payoff of 1. Carlos Deborah Left Left 4,4 Right 2,4 Right 6,7 5,1 The only dominant strategy in this game is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Carlos chooses and Deborah chooses
!
Analyze the following game. Create payoff bimatrices consistent with the information given. Explain your choices. Then find the maximin moves, all dominated strategies for all players. Game: Adam, Bill, and Cindy are registering for a foreign language class independently and simultaneously. The available classes are ITA100 and FRE100. They d not care much which, but they care with whom they share the class. Bill and Cindy want to be in the same class, but want to avoid Adam. Adam wants to be in the same class as Bill or Cindy, or even better, both.
Player 1 Cooperate (C) Defect (D) If the game has a dominant strategy, what is it? There is none. If the game has a Nash equilibrium in pure strategies, what is it? There is none. Cooperate (C) 3,3 8,0 Cooperate (C) is a dominant strategy for both players. Defect (D) is a dominant strategy for both players. Cooperate (C) is a dominant strategy for 1, and Defect (D) is a dominant strategy for 2. C, C is the only Nash equilibrium. D, D is the only Nash equilibrium. C, C and D, D are both Nash equilibria. Player 2 Defect (D) 0,8 1,1
Tyler and Pam are arrested and charged with armed robbery. The police interview both suspects separately about their involvement in the crime. Each suspect has to make a decision. They can betray the other suspect by confessing that they both committed the crime, or they can cooperate with the other suspect by remaining silent. The table shows the sentences that Tyler and Pam will receive given their choices. Use the table to answer the question. What will be the dominant strategy outcome for Tyler and Pam? They both get 10 years. Pam gets 5 years, and Tyler gets 15 years. O They both get 12 years. O Tyler gets 5 years, and Pam gets 15 years. Tyler Stay silent Confess Stay silent Pam gets 10 years Tyler gets 10 years Pam gets 15 years Pam Tyler gets 5 years Confess Pam gets 5 years Tyler gets 15 years Pam gets 12 years Tyler gets 12 years
Player 1 Cooperate (C) Defect (D) Cooperate (C) 3,3 8,0 Player 2 Defect (D) 0,8 1,1 In general, a combination of strategies is a Nash equilibrium if ... Every player is choosing a best response against the other players' strategies. Every player has a positive payoff. The players maximize the sum of their payoffs. The players choose identical strategies. If the game is repeated, which cooperative actions could benefit both players? O Both players choose C. Player 1 chooses C, Player 2 chooses D. O Player 1 chooses D, Player 2 chooses C. Both players choose D.
Solve parts 1(d) and 1(e) ONLY
Image attched
Consider the following static, single-shot game played between two cyclists, Chico and Loco, who find themselves riding towards each other down a narrow lane. Chico wants to pass by safely, and he can only do this by cycling on the opposite side of the lane to Loco. So, he has two options: to cycle on the Right of the lane, or to cycle on the Left. Loco meanwhile is having a bad day and wants to crash into Chico, and the way he can achieve this is by cycling on the same side of the lane as Chico. So again, he has two options: to cycle on the Right of the lane, or to cycle on the Left. He does not care at all about hurting himself if they collide. (c) By constructing the best response lines of both players, identify all Nash equilibrium outcomes in the above game i.e., in pure and mixed strategies. (d) Provide an intuitive interpretation of the equilibrium outcome(s) identified in part (c) above.