In the incomplete information version of the Game of Chicken (see Tadelis 2013, Section 12.2.1), players 1 and 2 drive toward eachother and just before impact they simultaneously decide whether to swerve to the right or continue driving head-on. If both playchicken, each gets a payoff of 0. If i continues to drive while j i plays chicken, then i get a payoff of 8 and j gets a payoff of 0.Finally, if both continue to drive head-on, then each gets 4 – k, where k represents the cost to each player. k could be, with equalprobability, either high or low. While the distribution of type is common knowledge, none of the two players knows whether the cost tothe other player is high or low.1. Denoting the high cost with H and the low cost with L, draw the extensive form of the game.2. Assuming H= 16 and L = 0, derive from the extensive form the normal form, and find the unique pure-strategy Bayesian Nashequilibrium.1. The Game of Chicken is not played just between teenagers in films; it is relevant whenever optimal behaviour depends onsome combination of each player's tendency to be aggressive and his belief about his opponent's tendency to beaggressive.

Chicken Game : Two Players : Player 1 & Player 2 Two strategies to choose : (Straight ) ,…

Answered: In the incomplete information version…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Hello, please help me to solve this Game Theory question. Thanks in advance! Hobby hunter Jack decides what to do the next weekend. He can either stay at home and watch movies (Movies), or call his friend Katherine to go hunting (Hunt). If he stays in, both Jack and Katherine get a payoff of 2. If he decides to hunt, he knows the situation with his friend will resemble a classic stag hunt game with simultaneous moves: Hunting a stag is better than hunting a rabbit, but it only works if they cooperate. The hunting subgame is captured as: Katherine Stag Rabbit Jack Stag 3 , 3 0 , 1 Rabbit 1 , 0 1 , 1 1. Write the normal form representation of the full game, including Jack’s initial decision.2. Identify any pure-strategy Nash equilibria. How does this compare to the pure strategy Nash equilibria of the hunting game alone?
Susan and Thomas are playing a one-shot simultaneous move game an infinite time horizons. The payoffs matrix of the game played at each time period is Thomas R (3, 3) (13, 0) Susan (0, 13) (8,8) R. where the first number in each cell is the payoff to Susan and the second number is the payoff to Thomas. A trigger strategy of playing the Nash equilibrium forever if either agent deviates from the cooperative agreement will result in (R, R) being played at every time period so long as both agents' discount factors exceed: Check
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?
Describe the game and find all Nash equilibria in the following situation: Each of two players chooses a non-negative number. In the choice (a1, a2), the payoff of the first player is equal to a1(a2 - a1), and the payoff of the second player is equal to a2(1 – a1 – a2).
A and B are competitors in the mobile phone industry. Both A and B have to decide whether to participate or not to participate in a Phone for the Future Trade Fair next month. The matrix payoff below shows the profits (USD million) corresponding to their actions. a) What is the Nash equilibrium of the above game? b) Is the Nash equilibrium Pareto Optima? Explain. c) Suppose B is pessimistic of A's rationality, what is B's strategy? Compare and comment on B's strategy in (a) and (c). A Participate Do not participate B Participate Do not participate 400,1000 200,200 500,500 1000,400
Return to the game between Monica and Nancy in Exercise U10 in Chapter 5. Assume that Monica and Nancy choose their effort levels sequentially instead of simultaneously. Monica commits to her choice of effort level first. On observing this decision, Nancy commits to her own effort level. What is the subgame - perfect equilibrium of the game where the joint profits are 5m + 4n+ mn, the costs of their efforts to Monica and Nancy are m2 and n2, respectively, and Monica commits to an effort level first? Compare the payoffs to Monica and Nancy with those found in Exercise U10 in Chapter 5. Does this game have a first-mover or second - mover advantage? Using the same joint profit function as in part (a), find the subgame - perfect equilibrium for the game where Nancy must commit first to an effort level. U10. Return to the game between Monica and Nancy in Exercise U10 in Chapter 5. Assume that Monica and Nancy choose their effort levels sequentially instead of simultaneously. Monica commits…
Consider a Prisoners' Dilemma game involving two players, N = {1,2}, each of whom may choose either to co-operate (C) or to defect (D). The payoffs this game are illustrated in the below table. Player 1 receives the first listed payoff in each cell while player 2 receives the second listed payoff in each cell. 2 с 3,3 4,0 D 0,4 1, 1 a. Solve for the pure strategy Nash equilibrium of this static game. Are the players able to co-operate with one another? Explain why or why not. Suppose now that the above game is repeated infinitely many times and let 8 > 0 denote the common discount factor between periods. Suppose that the two players make the following agreement: "Play C in every period. If D is ever played, play D in every period thereafter." b. Explain how the one-deviation principle can be used to check whether the above agreement represents a subgame perfect Nash equilibrium of the infinitely repeated game. c. Use the method described in part b. of this question to calculate the…
Consider the following 2-player normal form game. Player 2 Bananas Orange Player 1 Grapes 11, 3 8, 2 Apple 9, 7 6, 5 Player 1's dominant strategy is [Select ] and Player 2's dominant strategy is [ Select ) The Nash Equilibrium of this game is ( Select ) (select all that apply).
Mr. and Mrs. Ward typically vote oppositely in elections and so their votes “cancel each other out.” They each gain two units of utility from a vote for their positions (and lose two units of utility from a vote against their positions). However, the bother of actually voting costs each one unit of utility. Diagram a game in which they choose whether to vote or not to vote.
Player 1 and player 2 are playing a simultaneous-move one-shot game, where player 1 can move "up" or "down" and player 2 can move "left" or "right" The payoffs for the game are shown in the payoff matrix. The first number of each cell represents player 1's payoff, and the second number is player 2's. Use the matrix to answer the questions below. Player 1 2nd attempt Part 1 Part 2 Which of the following outcomes is a pure strategy Nash equilibrium of this game? P = (1-P) = Up Down Part 3 9= Left -16, -18 -20,7 Choose one or more: A. There is no pure strategy Nash equilibrium in this game. OB. Player 1 plays up; player 2 plays left. OC. Player 1 plays up; player 2 plays right. □ D. Player 1 plays down; player 2 plays left. O E. Player 1 plays down; player 2 plays right. Player 2 Suppose player 1 assigns probability p to playing up and (1 - p) to playing down. What do p and (1-p) have to be such that player 2 is indifferent between playing left and right? Round all answers to two decimal…
John and Paul are walking in the woods one day when suddenly an angry bear emerges from the underbrush. They each can do one of two things: run away or stand and fight. If one of them runs away and the other fights, then the one who ran will get away unharmed (payoff of 0) while the one who fights will be killed (payoff -200). If they both run, then the bear will chase down one of them and eat them to death but the other one will get away unharmed. Assuming they don't know which one will escape we will call this a payoff of -100 for both. If they BOTH fight, then they will successfully drive off the bear but they may be injured in the process (payoff -20). Construct a payoff matrix for this game and identify the pure strategy Nash equilibrium. (Indicate it with words not with a circle!)
Consider the following two player game. In each cell the first number refers to the payoff to Player 1 while the second number refers to the payoff to Player 2. Suppose the two players move simultaneously (at the same time). Which one of the following statements is CORRECT? Player #1 Player #2 Top Bottom Left 7.7 4.0 Right 0,4 4,4 O There are three equilibria in this game: two pure strategy equilibria at [Top, Left] and [Bottom, Right) and al third equilibrium in mixed strategies. In the mixed strategy equilibrium of this game. Player 1 should play Top with probability 2/5 and Bottom with probability 3/5; Player 2 should play Left with probability 2/5 and Right with probability 3/5. O There are three equilibria in this game; two pure strategy equilibria at (Top. Left) and (Bottom, Right) and a third equilibrium in mixed strategies. In the mixed strategy equilibrium of this game, both players should randomize over the strategies with probability and %. O There is a unique dominant…

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