B's profit B invests B does not invest 100 80 100 -40 -40 10 80 10 Which of the following statements are correct? Select one or more: O a. If A invests, B's best strategy is to not invest since A will take all the profit O b. Whoever invests first gains a first-mover advantage O c. The co-ordination game exhibits two Nash equilibria. O d. If B chooses to not invest, A's best strategy is also to not invest. A's profit A does not invest A invests
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- Player 2 C D A Player 1 2,3 В 6, —2 | 4, 3 7,8 Select the value corresponding to the probability with which player 2 plays C in the mixed strategy Nash equilibrium: O 1/8 O 1/6 1/5 O 1/4 1/3 1/2 2/3 O 3/4 4/5 O 5/6Exercise 6.8. Consider the following extensive-form game with cardinal payoffs: 1 R O player pay 000 2 1 M 3 b 010 O player 3's payoff 1 2 221 2 000 0 0 (a) Find all the pure-strategy Nash equilibria. Which ones are also subgame perfect? (b) [This is a more challenging question] Prove that there is no mixed-strategy Nash equilibrium where Player 1 plays Mwith probability strictly between 0 and 1.A st SW B st 2,1 5, 15 2. Consider the game of chicken above. SW 11,4 3,5 a. Find all Nash equilibrium in pure strategies. b. Say that player A uses a mixed strategy, where she picks st with prob. 0.55 and sw with prob. 0.45. What is B's expected payoffs from choosing pure st and pure sw? c. Player B uses a mixed strategy and wants A to choose sw. What is the minimum prob. p, for which B needs to play st so A will choose sw.
- 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.A Nash equilibrium occurs when O no player has an incentive to unilaterally change strategies. each player has an incentive to unilaterally change strategies. O both players can cooperate to increase their payoffs. O no player can earn a higher payoff from any other strategy.Player 2 E F H A 6, 5 6, 7 9, 6 7,6 В Player 1 C 6, 7 6, 9 8, 5 9, 7 5, 8 5, 6 7,5 7,5 7,9 8, 7 11, 6 5, 6 (1) In the Unique Nash equilibrium of this game, which strategy does Player1 play? And why? (2) In the Unique Nash equilibrium of this game, which strategy does Player2 play? And why? (3) Is this game dominance solvable? And Why? (4) Does this game have at least one inadmissible Nash equilibrium? And Why?
- 3 0: she makes a pront of $9 An is ISK AVCise and aunty she makes. Let P be the probability that it rains the day of the concert. Find the number P tha makes Ann indifferent between organizing the concert in the Club or at the Park. 8. Compute the mixed strategy Nash equilibrium of the game below: Bungle F2 # Zippy E Left Right DOD F4 Up 2,-1 R I 20 F3 $ BAG 3 4 -2,0 HOT % 5 F5 Down 3,1 T 4,-2 VO MacBook Air 6 F6 Y & 7 F7 * U 8Question 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.Which of the following is FLASE for an extensive form game with perfect information? A. All Nash equilibria has the property of non-credible threat B. Subgame perfect equilibrium eliminates non-credible threats O C. In a Nash equlibrium strategy, each agent's strategy is a contingent plan
- Consider the following classic game, called Hawk and Dove. Player 2 Hawk Dove Hewk 0,0 4,1 Player 1 Dove 1,4 33 Select all pure strategy Nash equilibria and check the corresponding option if you think there exists a mixed strategy Nash equilibrium too. O There exists also a mixed strategy Nash equilibrium O Hawk, Dove O Dove, Hawk O Hawk, Hawk O Hawk, Hawkage Which of the following statements is the best description of a Nash equilibrium? Select one: O a. An equilibrium outcome achieved by cooperation between players in the game b. An outcome that is achieved when players in the game have jointly maximized profits and divided those profits according to market share of each player O c. An outcome where each player's strategy depends on the behaviour of its opponents d. An outcome where each player's best strategy is to maintain its present behaviour given the present behaviour of the other players Next pageTwo companies are playing an entry game. In the first stage of the game the incumbent firm decides whether to invest in new robotic equipment, which will lower its marginal cost of production. In the second stage, a potential rival decides whether to enter the market. o If the incumbent firm chooses to invest and the rival firm does not enter the market, the incumbent makes 8 million in profits. o If the incumbent firm chooses to invest and the rival firm enters the market, the incumbent makes 2 million in profits, and the rival firm looses 1 million. o If the incumbent firm chooses NOT to invest and the rival firm does not enter the market, the incumbent makes 10 million in profits. o If the incumbent firm chooses NOT to invest and the rival firm enters the market, both the incumbent firm and the rival firm make 4 million each. (a) Draw a decision tree for this game. (b) Use backward induction to solve the game. What is the rival best strategy? What is the incumbent best strategy? (C)…