Problem 3 - The Perfect Subgame Find the set of pure strategy Nash equilibria and subgame perfect equilibria of the following game: Out In 0, 20 F A F A F A -5, -5 -1,8 8,5 10, 10
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- 3. Nash Equilibria Consider the following (normal-form) game. Compute a Nash Equilibrium of this game. U C D L | M R 5,0 1,3 4,0 2,4 1,4 3,5 0,1 1,0 5,0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?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.
- (1) equilibria Find the Nash equilibria of the games in Figures 1 and 2. Which of the Nash are subgame perfect? 1 0 E 2 71 2 Ch C F 3 2 E 2 H 0 C FIGURE 1 FIGURE 2 F 23 31 D G D 20 2 H 12. Find all pure and mixed strategy Nash equilibria of the following game. X Y Z X 4,2 0,0 0,1 0,0 2,4 1,3 Y3. 1 2 J K 2 1 2 0 0 K 3 3 E/ 1.1 2.2 B G 2 -2 a.) How many Subgames does this Game have? b.) Convert this Game Tree into matrix form. c.) Find all Pure Strategy Nash Equilibria of this Game. d.) Find all Subgame Perfect Nash Equilibria of this Game. (Pure and Mixed) 2 2.2
- 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 В2. Provide the normal-form expression to the extensive-form game below, and find all pure-strategy Nash equilibria there. Find the subgame-perfect Nash equilibrium then. A B X E Y B A B F t G F G BF B D A 0 3. Find the subgame perfect Nash equilibria (may or may not be unique) in the game below. A B 100 30 F 60 9 5 B 3 5 12 10 60 10 80 10 180 60 200 401. In the following extensive-form game, derive the normal-form game, and find all the pure-strategy Nash equilibria, subgame-perfect equilibria, and perfect Bayesian equilibria. L' M' R' 1 R L M 2 P M' R' 1,3 1,2 4,0 4,0 0,2 3,3 2,4
- on 8.1 Consider the following game: Player 1 A C D 7,6 5,8 0,0 Player 2 E 5,8 7,6 1, 1 F 0,0 1,1 4,4 a. Find the pure-strategy Nash equilibria (if any). b. Find the mixed-strategy Nash equilibrium in which each player randomizes over just the first two actions. c. Compute players' expected payoffs in the equilibria found in parts (a) and (b). d. Draw the extensive form for this game.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?1. Consider the following 2 person game H M L H 3,0 2,0 0,2 0,3 3,0 2,0 L 1,0 1,0 0,1 (a) Are there any pure strategy nash equilibria? If not, find the mixed strategy nash equilibrium. (b) In light of your answer above, are there any strategies which are not rationalizable?