a. What are the Nash equilibria of the game? Is this game a realistic one for an organisation? Explain your answer. What might an organisation do if it found itself in a situation similar to the one represented by this game.
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- 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…2. Cindy and Andy are both workers on a team. At the same time both workers can choose to work on the risky project (R) or the safe project (S). If both choose to work on the R project the payoffs are 5 to Cindy and 4 to Andy. If both work on the S project the payoffs are 4 to Cindy and 5 to Andy. If Cindy works on R and Andy on S, the payoffs are (8, 10) to Cindy and Andy respectively. Finally, if Cindy plays S and Andy plays R, the payoffs are (10, 7). a. What are the Nash equilibria of the game? Interpret your equilibria in terms of a firm using teams. b. Now assume that Cindy can move first and choose which project to work on. Andy observes Cindy's choice before making his choice of either R or S. What are the subgame perfect equilibria of the game? Interpret this sequential game in terms of communication and leadership in organisations.Suppose that the University of Alabama and Clemson are making spending decisions for theupcoming year. Assume that Alabama is currently spending $15 million on their recruiting andfacilities, and Clemson is spending $10 million. Each team has an additional $5 million to spendor keep as profits. If they both choose to not spend the additional $5 million then Alabama hasa 60% chance of getting the highest quality quarterback recruit to commit to them (getting thecommitment of the player is the goal). However, if they both choose to spend the additional $5million then there is a 57% chance that Alabama gets the high quality quarterback to commit. IfAlabama spends the additional $5 million but Clemson doesn’t then there is a 67% chanceAlabama gets the recruit. However, if Alabama does NOT spend the additional $5million butClemson does then there is a 50% change either team gets the recruit’s commitment. Setup thepayoff matrix and label the players, their strategies, and their payoffs, and…
- 2. Consider the following Bayesian game with two players. Both players move simultaneously and player 1 can choose either H or L, while player 2's options are G, M, and D. With probability 1/2 the payoffs are given by "Game 1" : GMD H 1,2 1,0 1,3 L 2,4 0,0 0,5 and with probability 1/2 the payoffs are according to "Game 2" : G |M|D H 1,2 1,3 1,0 L 2,4 0,5 0,0 (a) Find the Nash Equilibria when neither player knows which game is actually played. (b) Assume now that player 2 knows which one among the two games is actually being played. Check that the game has a unique Bayesian Nash Equilibrium.0 E F 3 2 FIGURE 2 23 D G 2 H 0 1 (2) Two friends, Albert (A) and Berta (B), have to decide on going to one of three bars, Xenia's (X), Yara's (Y), or Zana's (Z). They decide to select a bar by alternatively vetoing bars until one remains. First Albert vetoes a bar. If at least two bars remain, then Berta vetoes another bar. That process continues until a single bar remains unvetoed. Suppose Albert prefers Xenia's to Yara's to Zana's and Berta prefers Zana's to Yara's to Xenia's. Assume that, for each of the two, going to their most preferred bar gives a utility of 2, going to their next preferred bar gives a utility of 1, and going to their least preferred bar gives a utility of 0. Model this as an extensive form game and find its Nash equilibria. Which of the Nash equilibria are subgame perfect?** Please be advsed that this is practice only from previous yeasr *** Answers: (a) There are no Nash equilibria.(b) There are two pure strategy Nash equilibra, one with (H,H) and another with (L,L), and no mixed strategy Nash equilibria.(c) There are two pure strategy Nash equilibra, one with (H,H) and another with (L,L), and one mixed strategy Nash equilibria with p = 1/2 and q = 1/2.(d) There are two pure strategy Nash equilibra, one with (H,H) and another with (L,L), and one mixed strategy Nash equilibria with p = 1/2 and q = 3/4.(e) There are two pure strategy Nash equilibra, one with (H,H) and another with (L,L), and one mixed strategy Nash equilibria with p = 3/4 and q = 1/2.
- NE 2). Consider the following extensive form game between two players. (1,10) u D 1 B X (a) List all pure strategies of player 2. (b) Represent this game in normal form. (c) Find all pure-strategy Nash equilibria of this game. (d) Find all SPNE (in pure strategies) of this game. (6,3) (4,2) (5,1)Question 5 ave Answer Player 1 has two options: L and R. If Player 1 chooses L, then Player 2 has two options; she can choose A or B. If Player 2 chooses A payoffs are (2; 1) and if she chooses B payoffs are (1; 2). If Player 1 chooses R, then Player 2 has two options; she can choose Y or N. If Player 2 shows Y payoffs are (0; 3) and if she chooses N payoffs are (1; 2). Which of the following statements is true? O A. (L; B,Y ) is a subgame perfect equilibrium of this game O B. (R; B,N ) is a subgame perfect equilibrium of this game O C.(L; A,Y) is a subgame perfect equilibrium of this game O D. (R; B,Y ) is a subgame perfect equilibrium of this gameN=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…
- Question 28 Suppose the following game: I Player 1 nice nice Player 2 50, 50 mean 90,20 Which of the following is true? mean 20,90 30, 30 O Both players play "mean" with a 70 % chance, and "nice" with a 30% chance. O There is no Nash Equilibrium in pure strategies, there is only one Nash Equilibrium in mixed strategies. Both players play "nice" with a 70% chance, and "mean" with a 30% chance. There is no Nash Equilibrium in mixed strategies, there is only one Nash Equilibrium in pure strategies.(a) Stan and Ollie are two students who share a flat. Both of them prefer to live in a clean flat. However, neither is too fond of housecleaning. Each of them receives a payoff of 12 if they both clean the flat. If neither person cleans the flat, they receive a payoff of 6 each. If one person cleans the flat but the other person does not, then the payoff for the person who does the cleaning is 5 and the payoff for the person who doesn't do any cleaning is 15. (i) Write down the payoff matrix of this game. Derive the dominant strategy equilibrium. Is this also a Nash equilibrium? (ii) Expiain your reasoning. Consider a game with N players. Each player chooses Black or White. If a player (b) chooses Black, she gets 100 if everyone else also chooses Black, and she gets 0 if any of the other players does not choose Black. If a player chooses White, she always gets 50. Show that everyone choosing Black and everyone choosing White are both Nash equilibria of this game.Two farmers Anil and Bala are each deciding how to deal with pest insects that destroy the crops they cultivate in their adjacent fields. They have the choice of using either Integrated Pest Control (IPC) or Terminator (T). The payoffs for their choices in terms of tonnes of crop are shown in the diagram. Which of the following statements is incorrect? 5 Bala's payoff لنا 2 1 O 0 Select one: • 1 T.T 2 3 Anil's payoff 4 T.I 5 LI-Both use Integrated Pest Control (IPC) T.T-Both use Terminator T, I-Anil uses Terminator, Bala uses IPC LT-Anil uses IPC Bala uses Terminator a. Pareto-efficiency does not necessarily mean that we should approve of it. b. (1, 1) Pareto-dominates (T, T). c. (1, 1) and (I, T) are Pareto-efficient. d. If Anil and Bala moving from (T, T) to (1, 1), there is Pareto-improvement as both farmers are better off. e. Pareto criterion tells us that (1, 1) is the best outcome as it is Pareto-efficient.