The game of Chicken is played by two macho teens who speed toward each other on a single-lane road. The first to veer 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. Teen 1 Veer Does not veer Teen 2 Veer 2,2 3,1 Does not veer 1,3 0,0 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.

The game of Chicken is played by two macho teens who speed toward each other on a single-lane road. The first to veer 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. Teen 1 Veer Does not veer Teen 2 Veer 2,2 3,1 Does not veer 1,3 0,0 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.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.3P

See similar textbooks

Similar questions

You are playing a game with a friend. It’s yourmove but you don’t have a dominant strategy.Your payoff depends on what your friend doesafter your move. You consider flipping a coin todecide what to do. You are about to reach for acoin, but then you realize that your friend has adominant strategy. Explain how using backwardinduction (rather than a coin toss) will now determine your next move
In a gambling game, Player A and Player B both have a $1 and a $5 bill. Each player selects one of the bills without the other player knowing the bill selected. Simultaneously they both reveal the bills selected. If the bills do not match, Player A wins Player B's bill. If the bills match, Player B wins Player A's bill. a. Develop the game theory table for this game. The values should be expressed as the gains (or losses) for Player A. b. Is there a pure strategy? Why or why not? Determine the optimal strategies and the value of this game. Does the game favor one player over the other? d. Suppose Player B decides to deviate from the optimal strategy and begins playing each bill 50% of the time. What should Player A do to improve Player A’s winnings? Comment on why it is important to follow an optimal game theory strategy. с.
Two farmers, Ali and Hasan, graze their animals on a common land. They canchoose to use the common resource lightly or heavily and the resulting strategic interactionmay be described as a strategic form game. The payoff matrix is the following: (The table is attached on iamges part) Suppose that the game is repeated infinitely. If both players play a Grim-Trigger strategy, findthe discount factor δ such that (Light,Light) be a Nash equilibrium
10 1. Consider the game where initially She chooses between "Stay Home" and "Go Out". If She chooses "Stay Home" then She gets 2 and He gets 0. If She chooses "Go Out" then they each simultaneously choose "Movie" or "Concert" where the payoffs are 0,1 or 3 as in the Battle of the Sexes Game. What are the subgame perfect Nash Equilibria of this game ?
Sam and Sarah are thinking about getting married. However if either of them cheats on the other, they would get a payoff of 10, while the other person gets zero. If neither cheat, they stay with each other and get a payoff of 7 each and if both cheat, the relationship falls apart and each get a payoff of 1. What is the Nash equilibrium of this game? a. Cheat, Cheat b. Not cheat, Not cheat Sam cheats, Sarah doesn't Sarah cheats, Sam doesn't
Question 4. Zeynep and Mehmet will eventually play the following game. Mehmet L R U 3,1 0,0 Zeynep D 0,3 1,3 In a preliminary stage, Zeynep has already asked Mehmet to allow her to move first and proposed to pay him 1 unit of her own payoff in exchange. So Mehmet has to options: • If he accepts Zeynep's offer: they will play the sequential move version of the above game in which Zeynep moves first. Mehmet will receive 1 unit of utility more, and Zeynep will receive 1 unit of utility less (in any outcome of the game) compared to the payoffs given in the bimatrix. 2 • If he rejects Zeynep's offer: they will play the simultaneous move game. a. Represent this strategic interaction in a game tree. b. How many information sets does each player have? c. Characterize the set of pure strategies for both players. d. Present this game as a normal-form game, and characterize the set of pure strategy Nash equi- libria.
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.
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 Veer Don't Veer 2,2 3,1 1,3 0,0 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…
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.
please discuss the separation eqilibrium in details 1. Assume that two players play the Tinder game. There are two types of potential boyfriends: the gentleman (25% of the population) and the douchebag (75% of the population), and they can decide on the different level of effort: low, medium, and high. For the first type, the respective costs are 30, 50, and 80. For the second type, the respective costs are 50, 75, and 120. For the potential boyfriend, the payoff from being in relationship is 130, and the payoff associated with being dumped is 70. The girl can get 60 if she stays single, 100 if she is in relationship with the gentleman, and 25 if she dates the douchebag (credits to Owen Sims) a) Present the game in the extensive form b) Calculate the expected pay-off for the girl. Should she date at all? c) Discuss whether the game has a separating equilibrium
Anashequilibriumisastrategyprofilesuchthat: a)Both players are playing a best response strategy b)Both players must be playing a dominant strategyc)Both players achieve their highest possible payoff d)a) and c) e)b) and c)
Consider the following game : Stag Rabbit Stag 9, 9 0, 8 Rabbit 8, 0 7, 7 The first payoff is that of player 1 and the second that of player 2. a. ) Draw the extensive form of the simultaneous game. Find all the Nash equilibrium. p. Suppose player 1 moves first or we are in a sequential game now. Draw the extensive form in the sequential version. c. What is the subgame perfect Nash Equilibrium (SPNE) in the sequential version? d. ) Explain why it is an SPNE.