[3%]4. Consider the two-player game shown in the table below. Player 1 chooses between fourpossible strategies: A, B, C and D. Player 2 can choose among three possible strategies: a,b and c. In each cell of the table, the first number is the payoff for Player 1, the secondnumber is the payoff for Player 2. Higher numbers represent higher payoffs.Player 2abCA2,-24,0-6,-2BPlayer 14,-43,-39, 1C2,6-1,46,4D6,20,4-9,0(a) Simplify the game as far as possible using the iterated deletion of strictly dominatedstrategies. Clearly explain the steps of your reasoning.[2%](b) Identify any pure strategy Nash equilibria of the simplified game derived in part (a).[1%](c) Identify any mixed strategy Nash equilibria of the simplified game derived in part(a). Write down the best response function for each player. Draw these functionsPage 3 of 5

(b) Identify any pure strategy Nash equilibria of the simplified game derived in part (a).Nash…

Answered: [3%] 4. Consider the two-player game…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Cameron and Luke are playing a game called ”Race to 10”. Cameron goes first, and the players take turns choosing either 1 or 2. In each turn, they add the new number to a running total. The player who brings the total to exactly 10 wins the game. a) If both Cameron and Luke play optimally, who will win the game? Does the game have a first-mover advantage or a second-mover advantage? b) Suppose the game is modified to ”Race to 11” (i.e, the player who reaches 11 first wins). Who will win the game if both players play their optimal strategies? What if the game is ”Race to 12”? Does the result change? c) Consider the general version of the game called ”Race to n,” where n is a positive integer greater than 0. What are the conditions on n such that the game has a first mover advantage? What are the conditions on n such that the game has a second mover advantage?
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4. Finding Nash equilibria in sequential games Hubert and Larry are trying to decide what movie to see together. There are two theaters in town, each playing one movie. Hubert would prefer to see one movie (call it movie H) and Larry would prefer to see the other movie (movie L), but both would prefer to see one of the movies together rather than their preferred movies separately. As they are discussing where to meet, Larry's cell phone loses power, cutting the conversation short. Both movies start in 10 minutes; therefore, each person must decide which movie to see without being able to communicate with the other. The following payoff matrix represents the game they are playing. Hubert Movie H Movie L Hubert Larry Movie H 45, 30 0,0 Suppose Larry is near home and quickly starts charging his phone. At home, however, he gets terrible phone service but a strong wireless signal. Therefore, instead of calling Hubert, he uses a smartphone app to observe Hubert's location using GPS. Because…
Rita is playing a game of chance in which she tosses a dart into a rotating dartboard with 8 equal-sized slices numbered 1 through 8. The dart lands on a numbered slice at random. This game is this: Rita tosses the dart once. She wins $1 if the dart lands in slice 1, $2 if the dart lands in slice 2, $5 if the dart lands in slice 3, and $8 if the dart lands in slice 4. She loses $3 if the dart lands in slices 5, 6, 7, or 8. (If necessary, consult a list of formulas.) (a) Find the expected value of playing the game. | dollars (b) What can Rita expect in the long run, after playing the game many times? O Rita can expect to gain money. She can expect to win dollars per toss. Rita can expect to lose money. She can expect to lose dollars per toss. O Rita can expect to break even (neither gain nor lose money).
4. Consider the following extensive-form version of the Prisoner's Dilemma. In this version, Player 1 takes an action first. Player 2 then learns about Player 1's action and takes an action accordingly. The payoffs are represented as (7₁, 72), where 7₁ is Player 1's payoff and 72 is Player 2's payoff. Player 1 Speak Player 2 Silence Silence Player 2 Speak Speak (-8,-8) (0, -10) (-10,0) Which outcome is most likely to happen in the end of the game? (a) Player 1 plays Speak, Player 2 plays Speak (b) Player 1 plays Speak, Player 2 plays Silence (c) Player 1 plays Silence, Player 2 plays Speak (d) Player 1 plays Silence, Player 2 plays Silence (e) None of the above Answer: 4a. Silence (-1,-1)
6
For the Avranches Gap game given, find the security strategies and security payoffs for General Bradley and General von Kluge.
Consider the extensive form game show in the figure below. How many strategies does Player 2 have in this game? 6 Numerical answer a2 (2,2,1) 2 a1 b₂ 1 (2,4,2) 3 C₂ a3 by a2 d₂ (3,5,3) (3,1,2) b₂ b3 (4,2,0) (2,0,2) az (3) b3 (0,3,4)
9. For the payoff matrix below, consider a sequential version of the game in which Player 2 moves first and then Player 1 moves second. Which of the following is not a correct statement? Player 1 Top Center Bottom Left 1,2 5,1 6,0 Player 2 Middle 7,1 11,2 -4,3 Right 10,4 1,0 8,5 The subgame perfect payoffs coincide with those of a Nash equilibrium b. Depending on Player 2's move, Player 1 will sometimes optimally choose Bottom c. Player 2 will choose Right in the subgame perfect equilibrium d. Player 2 would be willing to pay a positive $ amount to move first rather than second e. Player 1 would be willing to pay a larger $ amount than Player 2 to move first
Q2
2. Consider the two-player strategic form game represented in the following payoff table: t 1 m b 7,2 1,2 3,7 2 M 2,4 3,4 1,6 R 1,3 7,1 4,2 Player 1 chooses between rows, S₁ = {t, m, b), and receives the first listed payoff in each cell. Player 2 chooses between columns, S₂ = {L, M, R), and receives the second listed payoff in each cell. a. Does either player have a strictly dominant strategy? Explain. b. Explaining your steps carefully, identify the set of rationalizable strategies in this game. c. Making sure to explain your solution method, solve for all pure strategy Nash equilibria in this game.
4. Consider the two-player Rock-Paper-Scissors game. Each player can choose between three pure strategies: Rock, Paper, and Scissors. Strategy Rock beats Scissors, but loses to Paper. Strategy Paper beats Rock but loses to Scissors. Strategy Scissors beats Paper, but loses to Rock. When the game is a draw, the payoff for the players is '0'. The payoff of winning is ‘+1' and the payoff of losing is '-1'. Formulate this problem as a two-person, zero-sum game by constructing a payoff table.

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