Suppose that you are a manager. You are considering whether or not to monitor employees with the payoffs in the normal-form accompanying game. Worker Work Shirk Manager Monitor -1,1 1,-1 Don't Monitor 1,-1 -1,1 Which of the following pairs of strategies constitutes a Nash equilibrium? Multiple Choice O Manager monitors and worker shirks. Manager does not monitor and worker works. Manager monitors and worker works. O None of the answers is correct.
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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.i. ii. QUESTION ONE A. A Nash equilibrium is a strategy profile such that every player's strategy is the best response to all the other players. It requires that each player makes a best response and that expectations regarding the play of other players are correct. Below is the table showing strategies and payoff for Player 1 and Player 2. PLAYER 1 R1 R2 R3 R4 C1 0,7 5,2 7,0 6,6 C2 2,5 3,3 2,5 2,2 PLAYER 2 C3 7,0 5,2 0,7 4,4 CA 6,6 2,2 4,4 10,4 REQUIRED; Transform the normal form game above into an imperfect extensive game form Find the Nash equilibrium for the game above using iterative deletion of strictly dominated strategies. Find the Nash equilibrium using brute force or cell by cell inspection.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?
- A principal can choose to make the allocation of tasks broad (B) or narrrow (N). At the same time an agent can choose to work put in high effort (H) or low effort (L). The payoffs are 20 to the principal and 30 to the agent is the actions chosen are B and L. For all other combinations of actions the payoffs are 0 to both players. Which of the following statements are true? DA Nash equilibrium of the game is (B, H) A Nash equilibrium is (N, L) There is no Nash equilibrium in pure strategies in this game. A Nash equilibrium is (N, H) A Nash equilibrium is (B, L)Consider the game below with a worker (W) and a firm (F). The worker initially can choose to acquire skills or not acquire skills. If the worker does acquire skills, the firm then gets to decide whether to compensate the worker or not. The extensive form of the game and the payoffs are below. Which of the following is true? W Acquirre Not Acquire There is no Nash equilibrium. C Compensate Not Compensate This game has a single Nash equilibrium. There are two Nash equilibria. None of the above. (0,0) Both players have a strictly dominant strategy. (10,10) (-5,20)Suppose you are interested in applying equilibrium theory to the following game, where 01 Nash equilibrium in which player 2 plays a sub-optimal action. {E, F}. Show that there is Bayesian Player 2 A • 1,1 GF Player 1 R • -1,0 NF 0,0 Nature A • 1,0 GE 1-p R -1, –1 NE 0,0
- Consider the payoff matrix for a game depicted below. Player 1 selects the row and Player 2 selects the column. Up Down Left 1, -1 -1, 1 Right -1, 1 1, -1 What is (are) the Nash equilibrium (equilibria)? Question 18Answer a. Player 1 plays right; Player 2 plays down b. Player 1 plays left; Player 2 plays down c. Player 1 plays down; Player 2 plays left d. Player 1 plays right; Player 2 plays up e. Player 1 plays up; Player 2 plays left f. There is no Nash equilibrium g. Player 1 plays down; Player 2 plays right h. Player 1 plays up; Player 2 plays right i. Player 1 plays left; Player 2 plays upJapan's Elpida Memory entered court management and was acquired by Micron. The media reportedthat it was the result of the semiconductor chicken game.■Question (a) Where is the Nash Equilibrium?■Question (b) What is the mixed-strategy equilibrium? – find out x and y■Question (c) What is the probability of a chicken game?Consider the game with the payoffs below. Which of the possible outcomes are MORE efficient than the Nash Equilibrium (NE)? Note, they do NOT need to be Nash equilibria themselves, they just need to be more efficient than the NE. Multiple answers are possible, but not necessary. You need to check ALL correct answers for full credit. JILL High Medium LowMAGGIE Left 3,4 2,3 2,2Center 4,8 9,7 8,7Right 7,6 8,5 9,4Group of answer choices (Left, Low) There is no strategy combination that is more efficient than the Nash equilibrium for this game. (Right, Medium) (Left, High) (Center, Medium) (Center, High) (Center, Low) (Left, Medium) (Right, Low) (Right, High)
- Sam and Sarah are thinking about getting married. However if either of them cheats on the other, they would get a payoff of 10, while the other person gets zero. If neither cheat, they stay with each other and get a payoff of 7 each and if both cheat, the relationship falls apart and each get a payoff of 1. What is the Nash equilibrium of this game? a. Cheat, Cheat b. Not cheat, Not cheat Sam cheats, Sarah doesn't Sarah cheats, Sam doesn'tGame Theory and Strategic Choices – End of Chapter Problem The Old Familiar and The Beehive are the only two bistros in town. Each is trying to decide whether or not it should advertise in the local newspaper. The accompanying payoff table gives their weekly profits under each possible outcome. The Beehive The Beehive does advertise does not advertise The Old Familiar The Old Familiar earns $X in profits. earns $3,500 in profits. The Old Familiar does advertise The Beehive The Beehive earns $Y in profits. earns $2,250 in profits. The Old Familiar The Old Familiar earns $2,000 in profits. earns $2,500 in profits. The Old Familiar does not advertise The Beehive The Beehive earns $4,000 in profits. earns $3,500 in profits. a. Which combination or combinations of X and Y would make a situation in which The Old Familiar does not advertise and The Beehive advertises a Nash equilibrium?10. Player A and Player B are playing a game . First , Player A chooses to either " Keep " or " Pass " . Second , Player B observes A's choice and Player B then chooses to either Keep or Pass . This process continues which creates the sequential game below . Please mark decisions that rational and selfish players will choose at every decision node ( 3 decisions by player A and 3 decisions by player B ) - mark them on the Figure . What is the equilibrium of this game ?