(i) Find all pure strategy Nash equilibria. (ii) Find the mixed strategy Nash equilibrium. (iii) What is the probability that both teenagers will survive?
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- (A) Two California teenagers Bill and Ted are playing Chicken. Bill drives his hot rod south down a one-lane road, and Ted drives his hot rod north along the same road. Each has two strategies: Stay or Swerve. If one player chooses Swerve he loses face; if both swerve, they both lose face. However, if they both choose Stay, they are both killed. The payoffs for the game of Chicken are given in the table below. Bill is the row player and Ted is the column player. Stay Swerve Stay -3, -3 2, 0 Swerve 0, 2 1, 1 (i) Find all pure strategy Nash equilibria. (ii) Find the mixed strategy Nash equilibrium. (iii) What is the probability that both teenagers will survive? Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.Consider the below payoff matrix for a game of chicken. Two players drive their cars down the center of the road directly at each other. Each player chooses SWERVE or STAY. Staying wins you more payoff only if the other player swerves. Swerving loses face if the other player stays. However, the worst outcome is when both players stay. Stay Swerve Stay -0,-0 -6,6 Swerve 6,-6 9,9 Player 1 chooses rows and Player 2 chooses columns. Denote the probability of "Stay" for Player 1 as p and for Player 2 as 9. What is the value of p so that Player 2 is indifferent between Stay and Swerve? Write your answer as a decimal number with 2 decimal places (e.g. 0.05)CLASSES OF GAMES First, Alice chooses either action al or action a2. If Alice chooses action al, then she receives a payoff of 2 and Bob receives a payoff of 8. If Alice chooses action a2, then Bob chooses either action b1 or action b2. If Bob chooses action b1, then Alice receives a payoff of 0 and Bob receives a payoff of 2. If Bob chooses action b2, then Alice receives a payoff of 4 and Bob receives a payoff of 4. Which of the following are correct statements about the game described in the previous paragraph? (Mark all that are correct.) This game has perfect information. The strategy profile (a2,b1) is a Nash equilibrium of this game. Bob's backward induction payoff is 8. The strategy profile (al,b1) is a Nash equilibrium of this game. The strategy profile (a1,b2) is a Nash equilibrium of this game. The strategy profile (a2,b2) is a Nash equilibrium of this game. This is a bargaining game. This is a promise game. This is a threat game. Alice's backward induction payoff is 2.
- Two workers are on a production line. They each have two actions: exert effort, E, or shirk, S. Effort costs a worker e > 0 and shirking costs them nothing. If two workers do action E a lot of output is produced and the workers earn £3 each. If only one worker chooses action E less output is produced and they both earn £1. The workers earn nothing if they both shirk. (i) Describe this situation as a strategic form game (assuming the workers do not observe each other's effort choice when making their own decision). (ii) For what values of e does this game have strictly dominant strategies? (iii) Describe the Nash equilibria of this game for e = 0,1, 2, 3. (iv) The workers now are re-arranged into a production line. First worker 1 moves and then worker 2 moves. Worker 2 can now see worker l's effort level before they choose their effort. Draw this extensive form game. (v) Find the subgame perfect equilibria of the production-line game for c = 1/2 and c = 3/2.The following table shows the payoff matrix that represents the strategic interaction between two classmates, Amelie and Brianna. They are deciding which Scottish island to visit on a day trip. Brianna Kerrera Cumbrae Amelie Kerrera 5, 2 1, 1 Cumbrae 3, 3 3, 5 a. Amelie likes Kerrera more than Cumbrae, conditional on both choosing the same island b. In a sequential game where Brianna can move first, Amelie would choose to visit Cumbrae c. In a one-shot, simultaneous game, both Amelie and Brianna will choose to visit Kerrera since their total happiness would be the highest d. There are two Nash equilibria2. Brad and Angelina have agreed to meet up for their first date. Neither of them can remember the exact location where they arranged to meet up and have forgotten their phones at home. Their payoff matrix can be described as follows: Brad The Hive Le Monde a) What is the Nash equilibrium in this game? Angelina The Hive 5; 5 0; 0 Le Monde 0; 0 5; 5
- Consider the following game represented in normal form. Terry and Kerry are roommates who must make decisions about cleaning. Terry's payoff is the fiırst number in each cell and a higher number is a better outcome. Assume that Terry and Kerry make their decisions simultaneously. Kerry Clean Don't clean Terry Clean ( 8, 2 ) ( 3, 5 ) Don't ( 10, 3) ( 4, 1 ) clean The Nash equilibrium of this game is Terry will [ Select ] v and Kerry will [ [ Select ]“To be or not to be, that is the question.” Imagine that in answering this question Hamlet had the following data to consider. Hamlet must choose either “To Be” or “Not to Be.” If Hamlet chooses “To Be” then his enemy the King will make a decision to either “Kill” Hamlet or let him “Live.” If Hamlet is killed by the King his payoff in this game is 200 since he will have been killed by the King who is his uncle and who also killed Hamlet’s father, the King’s brother, who was the prior king. If the King decides to let Hamlet Live then Hamlet will be able to avenge his father’s death and his payoff will be +300. Hamlet also considers suicide an option but given the uncertainty of the afterlife if he chooses not to be then his payoff is +100 since his doesn’t what the afterlife holds for one who kills himself. Draw the complete game tree for this situation. Be sure to accurately label the tree and include the payoffs. Assume Hamlet will choose the course of action that offers the highest…How do we solve a Sequential-move game?
- Three married couples in the state of Maryland—Bob and Carol, Ted and Alice, and Ross and Mike (remember, same-sex marriage is legal in the state of Maryland)—are thinking about renting a boat to go sailing on the Chesapeake Bay. The cost of a boat rental is $600. Each of the three couples puts some amount of money in an envelope. Thus, each player in this game is a couple. If the total amount collected is at least $600, then the boat is rented. If the amount collected is more than $600, then the money left over after renting the boat is spent on wine. If the total amount collected is less than $600, then they do not rent the boat, and the money is spent on a dinner. Assume the benefit to a couple from the boat trip is 400, the benefit from each dollar spent on wine is 50 cents, the benefit from each dollar spent on dinner is 40 cents, and the personal cost of the contribution to a couple equals the amount of contribution. For example, if the boat is rented, $50 of wine is purchased…Suppose that Green Giant and Red Rover are two companies competing in the canned vegetable market. Each is contemplating an aggressive new ad campaign. The payoffs of each decision are listed below, where Green Giant is player 1. Green/Red Ad Campaign No Ad Campaign |Ad Campaign |1 million, 1 million zero, 3 million No Ad Campaign 3 million, zero 2 million, 2 million What is the Nash equilibrium of the game? a. (advertise, don't advertise) b. (advertise, advertise) c. (don't advertise, don't advertise) d. (don't advertise, advertise)Consider the following simultaneous move game: Player 1 U M D Player 2 L 2,10 2,5 8,7 C 5,2 11,8 8,4 R 5,4 2,9 8,3 In the Nash equilibrium of this game, player 1 receives a payoff of ✓ and player 2 receives a payoff of
