2. Individual Problems 15-2 Mr. and Mrs. Ward typically vote oppositely in elections and so their votes "cancel each other out." They each gain 20 units of utility from a vote for their positions (and lose 20 units of utility from a vote against their positions). However, the bother of actually voting costs each 10 units of utility. The following matrix summarizes the strategies for both Mr. Ward and Mrs. Ward. Mr. Ward Mrs. Ward Vote Vote Mr. Ward: -10, Mrs. Ward: -10 Don't Vote Mr. Ward: -20, Mrs. Ward: 10 The Nash equilibrium for this game is for Mr. Ward to payoff of Don't Vote Mr. Ward: 10, Mrs. Ward: -20 Mr. Ward: 0, Mrs. Ward: 0 units of utility and Mrs. Ward receives a payoff of and for Mrs. Ward to units of utility. . Under this outcome, Mr. Ward receives a

2. Individual Problems 15-2 Mr. and Mrs. Ward typically vote oppositely in elections and so their votes "cancel each other out." They each gain 20 units of utility from a vote for their positions (and lose 20 units of utility from a vote against their positions). However, the bother of actually voting costs each 10 units of utility. The following matrix summarizes the strategies for both Mr. Ward and Mrs. Ward. Mr. Ward Mrs. Ward Vote Vote Mr. Ward: -10, Mrs. Ward: -10 Don't Vote Mr. Ward: -20, Mrs. Ward: 10 The Nash equilibrium for this game is for Mr. Ward to payoff of Don't Vote Mr. Ward: 10, Mrs. Ward: -20 Mr. Ward: 0, Mrs. Ward: 0 units of utility and Mrs. Ward receives a payoff of and for Mrs. Ward to units of utility. . Under this outcome, Mr. Ward receives a

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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1) Consider the following variant of the prisoner's dilemma with altruistic preferences. For simplicity, I'm adding 15 to the payoffs of the baseline normal form representation of the game we describe in class which results in the following: Player I\ Player 2 Cooperate Non-Cooperate Cooperate 8.8 0,15 Non Cooperate 15,0 14,14 Assume now that the players are not “selfish”; rather the preference of each player i are represented by the payoff (utility) function m; (a) + ßm; (a) where mi(a) is the payoff received by player i when the strategy profile is a, j is the other player, and ß is a given non-negative number. Player 1's payoff to the strategy profile (Cooperate, Cooperate), for example, is 8+8ß. A) Assume ß = 1. Write the normal form of the game. Is this game a prisoner's dilemma? What is the Nash equilibria of the game? B) Find the range of values of ß for which the resulting game is the prisoner's dilemma.
7. Which of the following is not true of the “Battle of the Sexes" Game? a. The predicted outcome demonstrates how independent and rational play by players can quickly reach an agreement or a convergence of expectations concerning which strategy will be played by each player in equilibrium. b. The Battle of the Sexes Game can be used to depict a variety of situations where the players' interests do not precisely coincide, except for the fact that they both want to avoid the outcomes that would result from choosing different actions from one another. c. Players do not have a dominant strategy but playing “Boxing" say, is a best response to the other playing "Boxing" even if it doesn't give the player the payoff associated with his or her preferred alternative. d. Played only once, the outcome where each goes to their preferred venue cannot be Nash Equilibrium.
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.
2. Consider the following two-player game with two players: Adam and Eve. Adam A1 A2 A3 A4 E1 6,3 5, 3 5, 0 2,0 E2 4,4 5, 4 3, 2 2, 3 Eve E3 4, 1 0,2 6, 1 3, 4 E4 3,0 5, 1 4,0 6₂ 1 a. Find the Iterated Elimination of Dominant Strategies Equilibrium for this game. Explain.
Please show me the correct answer and step, thank you so much for your help
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1. Consider a game of chicken: two players approach a narrow bridge with room only for one, and each chooses either to go through and hope the other guy backs off (call this action H, for "hawk"), or backs off to let the other go through (call this action D, for "dove"). If both players are normal, then each gets a payoff of -1 from a collision (i.e. if both choose H), 1 if they choose H against D, 0 if they choose D (regardless of what the other player chooses). Now perturb the game as follows: there is a chance p > 0 that P2 is a “violent type", who gets 1 from playing H regardless of Pl's action, and -1 from playing D, again regardless of P1's action. (a) Illustrate the game tree corresponding to the Harsanyi transformation of this game (i.e. the dynamic game of imperfect information in which nature moves first). (b) Illustrate the extended game (i.e. the normal form game corresponding to your game tree in part (a)). (c) Find all values of p for which there is a BNE in which P1…
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John and Jane usually vote against each other’s party in the SSC elections resulting to negating or offsetting their votes. If they vote for their party of choice, each of them gains four units of utility (and lose four units of utility from a vote against their party of choice). However, it costs each of them two units of utility for the hassle of actually voting during the SSC elections. A. Diagram a game in which John and Jane choose whether to vote or not to vote. B. Suppose John and Jane is in agreement not to vote during the election. 1.) Would such an agreement improve utility? Justify your answer. 2.) Would such an agreement be an equilibrium? Justify your answer.