1. Answer the following questions regarding a two-player game shown in the payoff matrix below. 2 S R S 3,3 0,1 R 1,0 1,1 (1) Derive all pure strategy Nash equilibria of the game. (2) Derive all (complete) mixed strategy Nash equilibria of the game. 2. Answer the following questions regarding a two-player game with perfect information shown below. 1 PI'S Payoff P2V Payoff (Note) P1 and P2 represent player 1 and player 2 respectively. (1) Write a normal form representation of the game and derive all pure strategy Nash equilibria. 2) Perive all pure strategy SPNE (subgame perfect Nash equilibria) of the game.

1. Answer the following questions regarding a two-player game shown in the payoff matrix below. 2 S R S 3,3 0,1 R 1,0 1,1 (1) Derive all pure strategy Nash equilibria of the game. (2) Derive all (complete) mixed strategy Nash equilibria of the game. 2. Answer the following questions regarding a two-player game with perfect information shown below. 1 PI'S Payoff P2V Payoff (Note) P1 and P2 represent player 1 and player 2 respectively. (1) Write a normal form representation of the game and derive all pure strategy Nash equilibria. 2) Perive all pure strategy SPNE (subgame perfect Nash equilibria) of the game.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.1P

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8) Find the mixed strategy Nash equilibrium of the following normal form game. Player 2 T1 T2 T3 2, 3 3, 5 1, 1 Player 1 S2 1, 4 4, 3 0, 5 Player 1 attaches probability (S1, S2) = () and Player 2 attaches probability (T1, T2, T3) = ( ) Player 1 attaches probability (S1, S2) = (.) and Player 2 attaches probability (T1, T2, T3) = (qi, 42, 1 – q1 – 92) where q1 , and 0 < q2 S %3D Player 1 attaches probability (S1, S2) = (G,;) and Player 2 attaches probability (T1, T2, T1) = (qı.42, 1 – q1 – 42) where 0 < qi <, and q2 = 3. Player 1 attaches probability (S1, S) = (;, -) and player 2 attaches probability (T1, T2, T3) = (1.42, 1- q1- 42) where 0 s qı s and q2 =
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.
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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
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