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- 5,3 4,4 3,6 7,6 Find the pure strategy nash equilibriaSuppose the following game is played infinite times in the future. Time discount is 0.90. What should be the value of x so that the equilibrium strategy is (Cooperate, Cooperate)? Player 2 Player 1 Cooperate Defect Cooperate (x, x) (2, 14) Defect (14, 2) (5, 5)What is the payoff for both players in the SPNE of this game?-(2,5)-(3,4)- (2,2)- (5,1)- (1,7)
- Japan'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?1. What is the expected value of playing this game ? a. The player repeatedly rolls a six - side d die until it comes up 6. b. When the die comes up 6 , the player receives a payoff, and the game ends. The player get s precise ly one payof f. c. The initial payoff is $6, and it increases by 20%. The f irst roll payoff is $6 ; the second roll payoff is $7.20 (1.2*$6) ; the third roll payoff is $8.64 (1.2*$7.20), and so on. What is the expected value of playing this game?Which of the following gambles is “unfair”? a. A game that promises to pay you $1 if a coin comes up head and cost you $1 if a coin comes up tail, with no entry fee. b. A game that promises to pay you $10 if a coin comes up head and cost you $1 if a coin comes up tail, with no entry fee. c. A game that promises to pay you $10 if a coin comes up head and cost you $1 if a coin comes up tail, with an entry fee of $4.50 for the right to play. d. All of the above.
- how do you do you find the expected payback for this problem? Find the expected payback for a game in which you bet $1010 on any number from 00 to 399.399. If your number comes up, you get $400400.onsider the game described by the ff table. what is thE best response for the column player if he/she knows that the row player will make the Y move?(a) Calculate the safety levels of both players.(b) Find the set of all Nash equilibria (pure and mixed).
- Question 1 Consider a first-price sealed bid auction of a single object with two biddersj = 1,2 and no reservation price. Bidder 1′s valuation is v1 = 2, and bidder 2′s valuation isv1 = 5. Both v1 and v2 are known to both bidders. Bids must be in whole dollar amounts.In the event of a tie, the object is awarded by a flip of a fair coin.(a) Find an equilibrium of this game.(b) Is the allocation of your answer to (a) efficient?Your company is competing in a sealed-bid auction for a package of items your company values at $30,000. You expect the bids to be uniformly distributed between $20,000 and $30,000. a. Fill in the following table Bid Profit P(Win)Competitors = 2 E(Profit)Competitors = 2 P(Win)Competitors = 3 E(Profit)Competitors = 3 $20,000 $22,000 $24,000 $26,000 $28,000 $30,000 b. If there are two competitors, what is the optimal bid? c. If there are three competitors, what is the optimal bid?Consider the following game 1\2 Y Z A 10,3 3,9 B 8,5 6,1 Suppose Player 2 holds the following belief about Player 1: θ1 (A,B) = (9/10,1/10) What is the expected payoff from playing ‘Y’ ? What is the expected payoff from playing ‘Z’ ? Based on these beliefs, player 2 should respond by playing _____