urgent ! 1,1 3,0 0,3 2,2 (a) Can strategy profile (B,D) be played at the first stage if the game is repeated twice with observable actions without a discount factor? Why? (b) For which values of the discount factor strategy pro le (B,D) can be played when the game is repeated infinitely many times?
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- please solve it in 30 minute please Consider an infinitely repeated game where the stage game is the game of chicken: Swerve Straight Swerve 0,0 -1,1 Straight 1, –1 -10, -10 Assume that the discount factor is very close to one. For concreteness, you can assume that d = 0.99. (a) Is there an SPE in which player l's payoff is 1/(1 – 6)? Explain. (b) Is there an SPE in which each player gets a payoff of 0? Explain. (c) Is there an SPE in which player l's payoff is -2/(1 – 8)? Explain.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.** Please be advsed that this is practice only from previous yeasr *** Answers: (a) There are no Nash equilibria.(b) There are two pure strategy Nash equilibra, one with (H,H) and another with (L,L), and no mixed strategy Nash equilibria.(c) There are two pure strategy Nash equilibra, one with (H,H) and another with (L,L), and one mixed strategy Nash equilibria with p = 1/2 and q = 1/2.(d) There are two pure strategy Nash equilibra, one with (H,H) and another with (L,L), and one mixed strategy Nash equilibria with p = 1/2 and q = 3/4.(e) There are two pure strategy Nash equilibra, one with (H,H) and another with (L,L), and one mixed strategy Nash equilibria with p = 3/4 and q = 1/2.
- Find all NE of the stage game.(b) Consider a two-period game without discounting in which the stage game is played ineach period. Find all pure strategy SPNE.(c) What’s the min-max payoff of each player?(c1) Consider pure strategies only.(c2) Consider all strategies, including the mixed ones.(d) Now suppose the stage game is repeated infinitely many times. Use the Fudenberg-Maskin Folk theorem to find all possible values of payoff that can be supported as aSPNE.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 5Consider the following extensive-form game. U D A B A B -6,6 X Y X Y P 3,8 -8, 1 1,2 -2, 1 5,5 -0,0 The dashed lines represent information sets. (a) Represent this game in normal-form. (b) Derive the Nash equilibria in pure strategies. (c) Describe the (proper) subgames of this game. (d) Derive the subgame perfect Nash equilibria in pure strategies.
- Consider the game matrix below.. E F -4, -5 5, 2 3, 1 1, 1 1, 6 4, 2 3, 7 1, -2 4, 3 А B C a) Perform best-response learning dynamics starting for 5 iterations from the initial strategy profile of . List the strategy profile played on each iteration below. Iteration 1: Iteration 2:see image Use the following setting for questions 1-3. Consider the following static game: C R L 3,1 0,0 5,0 T M 2,1 1,2 3,1 B 1.2 0,1 4,4 Suppose this game is played for two periods. At the beginning of period 2, the players can observe the outcome from period 1. There is no discounting. 1. First, assume only pure-strategy SPNE such that either player's second period strategy DOES NOT depend on the first period outcome. How many such SPNE are in this game? (a) 1 (b) 2 (c) 3 (d) 4 (e) none 2. Consider only SPNE from the previous question. What is the maximum sum of the players' payoffs that can be achieved in the first period? (a) 0 (b) 3 (c) 4 (d) 5 (e) 8 3. Now consider all possible pure-strategy SPNE such that (B,R) is played in the first period. What must be the equilibrium outcome in the second period of such SPNE? (a) (T,L) (b) (M,C) (c) (B,R) (d) (T,R) (e) There are no such SPNEConsider 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?
- 3. Find the saddle point, if it exists, for the following game. (b) Solve the following game by using the principle of dominance and find the probabilities of strategies for each player and the value of the game. Player B Player A II III IV V 3 4 4 II 2 4 III 4 4 IV 4 4 20 2420 8760NE 2). Consider the following extensive form game between two players. (1,10) u D 1 B X (a) List all pure strategies of player 2. (b) Represent this game in normal form. (c) Find all pure-strategy Nash equilibria of this game. (d) Find all SPNE (in pure strategies) of this game. (6,3) (4,2) (5,1)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.