Q: BI MATRIX GAME 7,4 2,8
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- 3) Consider the following two extensive form games and answer the following questions. How many subgames present in the following games? Find all pure strategies SPNE. Find all pure strategies NE of these games. Game A Game B u (5,3) u (0,2) 2 2 L L (-5,4) d (0,0) 1 1 1 (1,-5) (-10,-10) u R (2,3) A M 2 R 2 r d 1 (8,1) B (2,0) (2,2)U9. Consider a revised version of the game from Exercise S9: PROFESSOR PLUM Revolver Knife Wrench Conservatory 1,3 2,-2 0,6 MRS. PEACOCK Ballroom 3,2 1,4 5,0 (a) Graph the expected payoffs from each of Professor Plum's strategies as a function of Mrs. Peacock's p-mix. (b) Which strategies will Professor Plum use in his equilibrium mixture? Why? (c) What is the mixed-strategy Nash equilibrium of this game?a) Find the pure strategy Nash Equilibrium for the subgame starting at player l's second decision node. b) Find the Subgame Perfect Nash Equilibria for the entire game. 1 Withdraw Not 2 Withdraw Not Withdraw Not 10 2 6 2 10 Not Withdraw 2 Withdraw Not Withdraw Not 15 20 10 15 15 10 20 15 49
- 6) The following is a static game D 2,2 0,3 D 3,0 1,1 a) Convert this game into dynamic form game b) Find the Nash equilibrium and subgame perfect Nash equilibrium of this game. c) If you consider this game as dynamic then what kind of dynamic game is this.(a) Consider the following bimatrix of a normal form game. Show that the set of strategies that survive elimination of weakly dominated strategies depends on the order in which the weakly dominated strategies are eliminated. Player 2 L R 1,1 0,0 M| 1,1 0,0 | 2,1 Player 1 2,1 (b) Find an example of a game where the unique Nash equilibrium in pure strategies would not survive the eliminination of weakly dominated strategies. (c) Find an example of a game where both players' strategies are weakly dominated in the Nash equilibrium.Problem 3. For the following extensive form games (a) Find all the SPES of the following extensive-form games. (b) Turn each game into its strategic form and find all the PNES. Do they make sense in the initial game? (i) A M B C D E F G (1,0) (0, 1) (1,2) (4, 2) (2,0) (5, –1) (ii) L1 R1 (2,1) L2 R2 (1,2) L R (4, 1) (3,3) 2) (-)
- P2: Hawk Dove P1: Hawk -25, -25 50, 0 Dove 0, 50 15, 15 Is the mixed-strategy NE of the above game an evolutionary stable strategy (ESS)? Show your work and explain your answer.Question 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)16) Convert the following extensive form game into a normal form game. Solve the game to find all pure strategy Nash equilibria. 1 A B 2 W X Y 3, 3 1, 2 2, 1 4, 4
- Suppose now we alter the game so that whenever Colin chooses "paper" the loser pays the winner 3 instead of 1: rock paper scissors rock 0. -3 1 1. раper scissors -1 -1 3 (a) Show that xT= (,) and yT= (5) together are not a Nash equilibrium 3'31 for this modified 3'3 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.QUESTION (3) P1 R L P2 U P1 P1 R' L' R' L' (a) Find subgame perfect Nash equilibria of the game above. (b) Find all perfect Bayesian Nash equilibria and sequential equilibria of the game above.Consider the following sequential game: 1 O D,L U.L U,R U D,R D (0,2) 2 L What is the subgame perfect Nash equilibrium of this game? R. (-1,-1) (1,1)
