Consider the signaling game below. Does the game have a perfect Bayesian equilibriu which all sender types play L? Does there exist a perfect Bayesian equilibrium in which all sender types play R? Explain. 1,1 1,00 U Receiver L 4₂ R (1/3) Receiver 0,1 0,0
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- Consider the following simultaneous move game where player 1 has two types. Player 2 does not know if he is playing with type a player 1 or type b player 1. Player 2 C D Player 1 A 12,9 3,6 B 6,0 6,9 C D A 0,9 3,6 B 6,0 6,9 Type a Player 1 Prob = 2/3 Type b Player 1 Prob = 1/3 Find the all the possible Bayesian Nash Equilibriums (BNE) of this game.In the movie Rebel Without a Cause, James Dean and Buzz Gunderson compete for thefavours of sixteen year old Judy. Buzz's gang members steal two cars. The group of teenagers gathers on aLos Angeles lookout, with a cliff that drops down to the Pacific Ocean. James and Buzz are to drive the stolencars toward the cliff. The first person to jump from his car is declared the chicken (which is bad). The lastperson to jump is the hero (which is good), capturing Judy's affection and the gang's respect. The driverlesscars continue over the cliff and plunge to the rocks at its base.Each driver can make two possible actions. Jump when he feels endangered (be a chicken) or jump AFTERthe other driver jumps (be a rooster). Assuming that both feel endangered at the same moment, the followingmatrix represents the payoffs for James and Buzz for each choice of strategy.BuzzChicken RoosterJames Chicken 3, 3 -10, 20Rooster 20, -10 -50, -50 PLEASE ANSWER THE BELOW QUESTION WITH REFERECE TO THE ABOVE…Sophia is a contestant on a game show and has selected the prize that lies behind door number 3.The show’s host tells her that there is a 50% chance that there is a $15,000 diamond ring behindthe door and a 50% chance that there is a goat behind the door (which is worth nothing to Sophia,who is allergic to goats). Before the door is opened, someone in the audience shouts, “I will giveyou the option of selling me what is behind the door for $8,000 if you will pay me $4,500 for thisoption.” [Assume that the game show allows this offer.]a. If Sophia cares only about the expected dollar values of various outcomes, will she buythis option?b. Explain why Sophia’s degree of risk aversion might affect her willingness to buy thisoption
- 6. Battle of the Networks 1\2 %share Sitcom Sitcom 48;52 Sport 42;58 Nature 55:45 58;42 Ans: s; = (0; 0.85; 0.14); V, = 55.43 s; = (0.43; 0.57;0); V½ = 44.57 40;60 63;37 60;40 Sport Nature 56:44 52;48 Find Nash Equilibrium.10. Game theorylearn.canterbury.ac.nz Clasarsom Nov 15-ICO EUC LEARN | AKO See the game below and answer the questions 8 to 11: Player-1 C Player-2 X, Y Y Player-1 9 14 8. Player-2 16 17 16 Nash Equilibrium in this game: Select one: O a. Playert: C; Player2: X O b. Playert: C; Player2: Y Oc. Playert: L; Player2: X Od. Playert: L; Player2: Y e. None
- Use the decision tree below to answer the following question Aggression Lee: -10; Cody: -10 Cody Aggression Cooperation Lee: 40; Cody: 0 Lee Соорeration Aggression Lee: 0, Cody: 4o Cody Cooperation Lee: 25; Cody: 25 What is the Subgame Perfect Equilibrium (SPE) of this game? O {Lee: Aggression; Cody: Aggression} O {Lee: Aggression; Cody: Cooperation} O {Lee: Cooperation; Cody: Aggression} O {Lee: Cooperation; Cody: Cooperation}N=2 video broadcasting websites, You and Twi, must decide the number of minutes of ads to be displayed for every video that the user elects to watch. Let tY be the number of ad-minutes per video set by You, and tT the number of ad-minutes per video set by Twi. Streaming one video costs You cY=0.02, while it costs Twi cT=0.03. There are 100 million potential users, and each watches videos according to the following demand curves: qY((tY,tT) =10-2tY+tT=10-2tT+tY a- What is the cross-price elasticity between You and Twi? b- Suppose, for now, that You and Twi enter an (illegal) agreement by which they set tY=tT=t Derive the total number of users in the market as a function of t. Derive the profits for each website as a function of t. c- Now let the two platforms compete by each setting their number of ad-minutes: i. What is the best reply of You? What is the best reply of Twi? ii. Find the Nash Equilibrium of the game. iii. How many total users choose You and how many total users choose…L 0 4 15.1 X₂ A M R 0 1 4 0 2 B L 4 0 с X3 M R 0 1 3 FIGURE 15.5 Exercise 15.1. Equilibrium Selection: Consider the extensive-form game in Figure 15.5. a. Find all the Bayesian Nash equilibria of this game. b. Which of the Bayesian Nash equilibria are also perfect Bayesian equi- libria? Why?
- Subgame Perfect Equilibrium. Stephen J. Seagull must decide whether or not to start a new movie project. If he decides not to, he and Clod VandeCamp both get a utility of 10. If he decides to begin the project, both he and Clod must simultaneously decide who the director should be: George Spellbinder, or Ed Tree. If they disagree on the director, the movie isn't made, but both have wasted time, so they get only a utility of 0. If they agree on George Spellbinder, the movie will be a roaring success, and each gets a utility of 20. If they agree on Ed Tree, the movie will be terrible. and they will only get a utility of 5. (a). Draw the extensive form of this game. (b). Write down the normal form. (c). Find all Nash equilibria. (d). Apply the theory of iterated elimination of weakly dominated strategies and state its prediction. (e). Find all the subgame perfect equilibria.You and a coworker are assigned a team project on which your likelihood or a promotion will be decidedon. It is now the night before the project is due and neither has yet to start it. You both want toreceive a promotion next year, but you both also want to go to your company’s holiday party that night.Each of you wants to maximize his or her own happiness (likelihood of a promotion and mingling withyour colleagues “on the company’s dime”). If you both work, you deliver an outstanding presentation.If you both go to the party, your presentation is mediocre. If one parties and the other works, yourpresentation is above average. Partying increases happiness by 25 units. Working on the project addszero units to happiness. Happiness is also affected by your chance of a promotion, which is depends on howgood your project is. An outstanding presentation gives 40 units of happiness to each of you; an aboveaverage presentation gives 30 units of happiness; a mediocre presentation gives 10 units…Two friends are deciding where to go for dinner. There are three choices, which we label A, B, and C. Max prefers A to B to C. Sally prefers B to A to C. To decide which restaurant to go to, the friends adopt the following procedure: First, Max eliminates one of three choices. Then, Sally decides among the two remaining choices. Thus, Max has three strategies (eliminate A, eliminate B, and eliminate C). For each of those strategies, Sally has two choices (choose among the two remaining). a.Write down the extensive form (game tree) to represent this game. b.If Max acts non-strategically, and makes a decision in the first period to eliminate his least desirable choice, what will the final decision be? c.What is the subgame-perfect equilibrium of the above game? d. Does your answer in b. differ from your answer in c.? Explain why or why not. Only typed Answer
