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- し(5,3) b I(2,2) も(0,0) (4,12) a (12.4) (0,0) i). List all subgame pertect Nash equilibria and name one Nash eqvilibrivm that is not subgame pertect i). How many strategies does playot and player 2 have?a W 3,5 3,4 8,4 0,0 3,3 8,9 y 0,1 5,9 9,8 Describe a strategy for player 1 that dominates x. O (1/3.0. 2/3) 1.0,0) O01.1) toUse the mixed method (Nash Equilibrium) to determine the following: What percentage of time should the maximizer play strategy H? 1. H6 17 ! 12 10 18.8% 84.6% O 15.4% 11.8%
- Which of the following conditions correctly describes a Nash equilibrium when two firms are in the market? Multiple Choice n91s1. $2)2 (51. $2) for all s1 and 12(51, $2)212(51. 52) for all s2. aqls1, s2)22(s1, s2) for all s1 and a2(s1, 52) 2 n1ls1.52) for all s2. Rylsi. s2)2 als1. 52) for all s as1. 52)22(1. s2) for all sy and a2(s. s2)2 a1(s1, s2) for all s2Question 1 Consider the following game. Find all Nash equilibria, subgame perfect Nash equilibria, and weak perfect Bayesian equilibria in pure and mixed strategies. a P2 (12, 12) b (12,-8) (7.-3) P1 m d (-3,2) r P2 C (2,7) d (22,17)Q2 Consider the following game. (a) Find all pure-strategy Nash equilibria. (b) Find all mixed-strategy Nash equilibria. 2, 4 6, 0 5,1 1,9 A В
- Exercise 6.1Suppose that two airlines decide to collude. Analyse the game between these two companies. Suppose that each of them can charge for tickets a high price or a low price. If one of them charges 100 euros, it gets few profits if the other also charges 100 euros and high profits if the other charges 200 euros. On the other hand, if the company charges 200 euros, it obtains very little profit if the other charges 100 euros and an average profit if the other also charges 200 euros. a) Represent the matrix of results of this game. b) What is the Nash equilibrium in this game? Explain your answer. c) Is there an outcome that would be better than the Nash equilibrium for the two airlines? How could it be achieved? Who would lose out if it were reached?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.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.
- li5,3,2) A (0,1, 1) -(3,2,6) (0.6,5) Y(2,1,4) R /6,3,0) -40,6) -(3,1,7) Is there Subgame Perlact Nash Equilibaion! I se what s it? 30,MIXED STRATEGY NASH EQUILIBRIUM Consider the following game in strategic form. b1 b2 a1 19,1 80,70 a2 40,50 1,19 1-п 1-0 This game has a mixed strategy Nash equilibrium (7*, o*) in which each player uses both pure strategies with strictly positive probability. Find the value of o*-n*. (Please report your answer in decimal form, rounded if necessary to the nearest 0.01.) Answer:Question Completion Status: II -10 -20 3. -30 -10 2. -20 3 -30 Write a normal form for this game. How many pure-strategy Nash Equilbria are there in this game? OA1 OB.2 OC3 OD.4 OES OF. More than 5
