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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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…
Refer to Table Left-Right-ZigZag. How many pure strategy Nash equilibria does this game have? Table: Left-Right-ZigZag Player 1 Drive left Driver right Zigzag 1) 1 2) 2 3) 3 4) 4 5) None of the above. Drive left (1,1) (-1,-1) (0,0) Player 2 Driver right (-1,-1) (1,1) (0,0) Zigzag (0,0) (0,0) (0,0)
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).
Once again, two ice cream truck vendors, A and B, are playing a simultaneous pricing game. If only one of the vendors prices low, he gets all the customers for a payoff of 12, while the other vendor gets no customers and a payoff of zero. If both vendors price high, they each get a payoff of 6. If both price low, they each get a payoff of 5. Suppose that the above game is repeated indefinitely, and together the vendors adopt a trigger strategy such that they would start charging the low price only if the other vendor charged a low price last time. Provided that the vendors stick to their new strategy, what would be the Nash equilibrium going forward? a) Both the vendors price high b) Both the vendors price low c) Vendor A prices high, vendor B prices low d) Vendor B prices high, vendor A prices low
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.
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…
Consider a simultaneous move game with two players. Player 1 has three possible actions (A, B, or C) and Player 2 has two possible actions (D or E.) In the payoff matrix below, each cell contains the payoff for Player 1 followed by the payoff for Player 2. Identify any pure strategy Nash Equilibria in this game. If there are none, state this clearly.
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.
Keith and Blake play a simultaneous one-shot game. Keith chooses between Top and Bottom, whereas Blake chooses between left and right. Payoffs are given by (Keith's payoffs are listed first and Blake's payoffs second): Top+left: 3,-6. Top+right:0,-7 Bottom+left:4,0. Bottom+right:-2,6. In a mixed strategy equilibria, Keith will play Top with what probability? 1. 6/7 2. 1/4 3. 1/2 4. 1/7 5. 0 6. 3/4
Consider the 2-player, zero-sum game "Rock, Paper, Scissors". Each player chooses one of 3 strategies: rock, paper, or scissors. Then, both players reveal their choices. The outcome is determined as follows. If both players choose the same strategy, neither player wins or loses anything. Otherwise: • "paper covers rock": if one player chooses paper and the other chooses rock, the player who chose paper wins and is paid 1 by the other player. "scissors cut paper": if one player chooses scissors and the other chooses paper, the player who chose scissors wins and is paid 1 by the other player. "rock breaks scissors": if one player chooses rock and the other player chooses scissors, the player who chose rock wins and is paid 1 by the other player. We can write the payoff matrix for this game as follows: rock paper scissors rock 0 -1 1 paper 1 0 scissors -1 1 -1 0 2. Suppose now we alter the game so that whenever Colin chooses "paper" the loser pays the winner 3 instead of 1: rock paper…

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