4. Consider the following game. There are two players and two possible simultaneous move games A and B. Player 1first chooses which game is to be played; both player observe which game is played and choose their strategy. Thepayoff matrices for Game A and B are given by :where k>>0.Game AUDL(10,5)(0,0)R(0,0)(5,10)Game B:UD(a) Write down the extensive form of this game.(b) Assume k = 2. Solve for all subgame perfect Nash equilibria of this game.L R(kk) (0,0)(0,0) (0,0)(c) Can you find a value of k such that there exists a SPNE in which player 1 chooses game B? Can you find a valueof k such that all SPNE involve player 1 choosing game B?

To write down the extensive form of the game, we need to represent the sequential order of moves and…

(a) Write down the extensive form of this game. (b) Assume k = 2. Solve for all subgame perfect Nash equilibria of this game. (c) Can you find a value of k such that there exists a SPNE in which player 1 chooses game B? Can you find a value of k such that all SPNE involve player 1 choosing game B?

(a) Write down the extensive form of this game. (b) Assume k = 2. Solve for all subgame perfect Nash equilibria of this game. (c) Can you find a value of k such that there exists a SPNE in which player 1 chooses game B? Can you find a value of k such that all SPNE involve player 1 choosing game B?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

4. Consider the following game. There are two players and two possible simultaneous move games A and B. Player 1
first chooses which game is to be played; both player observe which game is played and choose their strategy. The
payoff matrices for Game A and B are given by :
where k>
>0.
Game A
U
D
L
(10,5)
(0,0)
R
(0,0)
(5,10)
Game B:
U
D
(a) Write down the extensive form of this game.
(b) Assume k = 2. Solve for all subgame perfect Nash equilibria of this game.
L R
(kk) (0,0)
(0,0) (0,0)
(c) Can you find a value of k such that there exists a SPNE in which player 1 chooses game B? Can you find a value
of k such that all SPNE involve player 1 choosing game B?

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