Consider the following entry game between an incumbent (1, blue payoff) and an entrant (E, green payoff). If 5<2/3, then the entrant enters the market in equilibrium. True or False? E fight E leave True False enter out no fight (120+ 8 120, 0) E stay (20+8120, -30) (80 +880, -30 +840)
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Economic
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- Consider the following entry game between an incumbent (I, blue payoff) and an entrant (E, green payoff). If 8<2/3, then the entrant enters the market in equilibrium. True or False? E E leave fight True False enter no fight E out stay (20 + 8 120, -30) (80 +880, -30 + 840) (120 + 8 120, 0)rock paper scissors гock 0. -3 1 рарer 1. -1 scissors -1 3 0. (a) Show that xT= ( ) and yT= (3) together are not a Nash equilibrium 3 3 313 for this modified game. (b) Formulate a linear program that can be used to calculate a mixed strategy x € A(R) that maximises Rosemary's security level for this modified game. (c) Solve your linear program using the 2-phase simplex algorithm. You should use the format given in lectures. Give a mixed strategy x E A(R) that has an optimal security level for Rosemary and a mixed strategy y E A(C) that has an optimal security level for Colin.Exercise 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.
- Consider the following game: Player 2 In Out Player 1 In -2,-2 2, 0 Out 0, 2 0, 0 (a) What is the Nash equilibrium of this game, or what are the Nash equilibriaof this game? (b) Does either firm have a dominate strategy (a strategy that is always abest response)? Which? (c) Suppose Player 1 could move before Player 2 and Player 2 could observe Player 1’s move. What do you think would happen?Question 30 Consider the following Extended Form Game: O True A O False (2,3) P1 A' (5,5) A' (3,8) B A P2 B' P2 B' P1 B (1,9) Player 2 threatens to play (A',B') no matter what. Is this threat credible? (9,1)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?
- Consider the following simultaneous game: Player 1 U D Player 2 L 20,-10 -10, 20 R -10, 20 20,-10 Please indicate whether each of the following statements is true or false. Player 1 has a dominant strategy. This game has a Nash equilibrium. This game has a Nash equilibrium in pure strategies. Player 1's best response is D if player 2 plays R.For the friend-foe game, recall that there were 3 Nash equilibria possible, but the equilibria set didn't include the cooperative outcome, for which both players would win. Friend Foe Friend 500,500 0,1000 Foe 1000,0 0.0 a) If the game is played répeatedly. propose a play strategy that will enforce cooperation. For what valucs of o (discount factor) the equilibrium will be (Friend. Friend)?Convert into Normal-Form Game and Find out the subgame-Nash Equi- libria? OUT (0, 2) Small Entrant Small IN Entrant Incumbent Large Large Small Large (−6, −6) (−1,1) (1,−1) What does the Information set imply in this game? (-3,-3)
- ITERATIVE DOMINANCE Consider the following game in strategic form. a₁ 22 a3 bi 35,52 30,30 28,9 (9,11) (45,47) (47,28) (52,16) (28,9) (30,30) (16,45) (11,35) (35,52) b2 11,35 9,11 16,45 b3 52,16 45,47 47,28 Which of the following payoff profiles survive iterative deletion of strictly dominated strategies? (Mark all profiles that survive.)Consider the following two-player game with three options for each player. (Payouts are listed for the row player first, then the column player.) player Y layery 3,3 A 1,5 4,4 6,2 K 8,1 3,7 5,2 0,6 1,1 Find a mixed Nash equilibrium for this game. Solution suggestion: Use two variables per player. If p and are the probabilities of selecting the first two strategies, then 1-p-q is the probability of selecting the third strategy. You will need to solve a system of equations.Refer to the accompanying game. Firm A Which of the following is true? Multiple Choice O O O Low Price High Price O None of the answers is correct. Firm B Low Price (10,9) (-10,7) A dominant strategy for firm A is "high price." 19 There does not exist a dominant strategy for firm A. A dominant strategy for firm B is "low price." High Price (15,8) (11,11)