To Vote or Not to Vote 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. Mrs. Ward vote. don't vote Mr. Ward Vote. -1, -1. 1, -2 don't vote. -2, 1. 0,0?
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To Vote or Not to Vote
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.
Mrs. Ward
vote. don't vote
Mr. Ward Vote. -1, -1. 1, -2
don't vote. -2, 1. 0,0?
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- Mr. and Mrs. Ward typically vote oppositely in elections and so their votes “cancel each other out.” They each gain 4 units of utility from a vote for their positions (and lose 4 units of utility from a vote against their positions). However, the bother of actually voting costs each 2 units of utility. The following matrix summarizes the strategies for both Mr. Ward and Mrs. Ward. Mrs. Ward Vote Don't Vote Mr. Ward Vote Mr. Ward: -2, Mrs. Ward: -2 Mr. Ward: 2, Mrs. Ward: -4 Don't Vote Mr. Ward: -4, Mrs. Ward: 2 Mr. Ward: 0, Mrs. Ward: 0 The Nash equilibrium for this game is for Mr. Ward to (vote/not vote) and for Mrs. Ward to (vote/not vote) . Under this outcome, Mr. Ward receives a payoff of ____ units of utility and Mrs. Ward receives a payoff of ____ units of utility. Suppose Mr. and Mrs. Ward agreed not to vote in tomorrow's election. True or False: This agreement would increase utility for each spouse, compared to the Nash…Mr. and Mrs. Ward typically vote oppositely in elections and so their votes “cancel each other out.” They each gain 6 units of utility from a vote for their positions (and lose 6 units of utility from a vote against their positions). However, the bother of actually voting costs each 3 units of utility. The following matrix summarizes the strategies for both Mr. Ward and Mrs. Ward. Mrs. Ward Vote Don't Vote Mr. Ward Vote Mr. Ward: -3, Mrs. Ward: -3 Mr. Ward: 3, Mrs. Ward: -6 Don't Vote Mr. Ward: -6, Mrs. Ward: 3 Mr. Ward: 0, Mrs. Ward: 0 The Nash equilibrium for this game is for Mr. Ward to and for Mrs. Ward to . Under this outcome, Mr. Ward receives a payoff of units of utility and Mrs. Ward receives a payoff of units of utility. Suppose Mr. and Mrs. Ward agreed not to vote in tomorrow's election. True or False: This agreement would decrease utility for each spouse, compared to the Nash equilibrium from the previous part of the question. True…Mel and Mine usually vote against each other’s party in the SPG 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 SPG 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? Why? 2.) Would such an agreement be an equilibrium? Why?
- Mr. and Mrs. Ward typically vote oppositely in elections and so their votes "cancel each other out." They each gain 30 units of utility from a vote for their positions (and lose 30 units of utility from a vote against their positions). However, the bother of actually voting costs each 15 units of utility. The following matrix summarizes the strategies for both Mr. Ward and Mrs. Ward. Mr. Ward Vote Don't Vote Mrs. Ward Vote Mr. Ward-15, Mrs. Ward: -15 Mr. Ward: 30, Mrs. Ward: 15 The Nash equilibrium for this game is for Mr. Ward to payoff of False Don't Vote Mr. Ward: 15, Mrs. Ward: -30 Mr. Ward: 0, Mrs. Ward: 0 units of utility and Mrs. Ward receives a payoff of This agreement not to vote. Suppose Mr. and Mrs. Ward agreed not to vote in tomorrow's election. True or False: This agreement would decrease utility for each spouse, compared to the Nash equilibrium from the previous part of the question. O True and for Mrs. Ward to units of utility a Nash equilibrium, Under this outcome, Mr.…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, and determine the Nash Equilibrium.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.
- 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.The chicken game has often been used to model crises. Recall that in this game, the two players drive straight at each other. They can choose to swerve or keep going straight. If one swerves, and the other goes straight, assume that the one that swerves gets -10 utility and the one that goes straight gets 10 utility, since the one that swerves is deemed the loser. If both swerve, both get 0 utility. If both go straight, they crash and get -50 utility. Assume both players have a discount rate of 0.9 Draw the stage game of date night List all pure strategy Nash equilibria of the single stage game Consider an infinite horizon version of Chicken. Can you get an SPNE in which the both players swerve using a grim trigger type strategy? Consider the following strategies: both players swerve, as long as neither ever went straight. If one player ever plays straight, in all subsequent rounds the player that swerved goes straight and the player that went straight swerves. Can you think…Mr. Ward and Mrs. Ward typically vote oppositely in elections, so their votes “cancel each other out.” They each gain 10 units of utility from a vote for their positions (and lose 10 units of utility from a vote against their positions). However, the bother of actually voting costs each 5 units of utility. The following matrix summarizes the strategies for both Mr. Ward and Mrs. Ward. Using the given information, fill in the payoffs for each cell in the matrix. For example, in the top left cell, fill in the payoffs for Mr. Ward and Mrs. Ward if they both vote. (Hint: Be sure to enter a minus sign if the payoff is negative.) Mrs. Ward Vote Don't Vote Mr. Ward Vote Mr. Ward: , Mrs. Ward Mr. Ward: , Mrs. Ward Don't Vote Mr. Ward: , Mrs. Ward Mr. Ward: , Mrs. Ward
- Mr. and Mrs. Ward typically vote oppositely in elections and so their votes "cancel each other out." They each gain 24 units of utility from a vote for their positions (and lose 24 units of utility from a vote against their positions). However, the bother of actually voting costs each 12 units of utility. The following matrix summarizes the strategies for both Mr. Ward and Mrs. Ward. Mr. Ward Vote Vote Mrs. Ward Mr. Ward: -12, Mrs. Ward: -12 Don't Vote Mr. Ward: -24, Mrs. Ward: 12 The Nash equilibrium for this game is for Mr. Ward to payoff of Don't Vote Mr. Ward: 12, Mrs. Ward: -24 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 aSuppose players A and B play a discrete ultimatum game where A proposes to split a $5 surplus and B responds by either accepting the offer or rejecting it. The offer can only be made in $1 increments. If the offer is accepted, the players' payoffs resemble the terms of the offer while if the offer is rejected, both players get zero. Also assume that players always use the strategy that all strictly positive offers are accepted, but an offer of $0 is rejected. A. What is the solution to the game in terms of player strategies and payoffs? Explain or demonstrate your answer. B. Suppose the ultimatum game is played twice if player B rejects A's initial offer. If so, then B is allowed to make a counter offer to split the $5, and if A rejects, both players get zero dollars at the end of the second round. What is the solution to this bargaining game in terms of player strategies and payoffs? Explain/demonstrate your answer. C. Suppose the ultimatum game is played twice as in (B) but now there…Let us see the example of Juan and María given but modify their preferences. It is still the case that they are competitive and are deciding whether to show up at their mom’s house at 8:00 A.M., 9:00 A.M., 10:00 A.M., or 11:00 A.M. But now they don’t mind waking up early. Assume that the payoff is 1 if he or she shows up before the other sibling, it is 0 if he or she shows up after the other sibling, and it is 1 if they show up at the same time. The time of the morning does not matter. Find all Nash equilibria.