Answered: In a two-player, one-shot…

Name: In a two-player, one-shot simultaneous-move game each player can choos
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Description: In a two-player, one-shot simultaneous-move game each player can choose strategy A or strategy B. If both players choose strategy A, each earns a payoff of $400. If both players choose strategy B, each earns a payoff of $200. If player 1 chooses stra

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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In a two-player, one-shot simultaneous-move game each player can choose strategy A or strategy B. If both players choose strategy A, each earns a payoff of $400. If both players choose strategy B, each earns a payoff of $200. If player 1 chooses strategy A and player 2 chooses strategy B, then player 1 earns $100 and player 2 earns $600. If player 1 chooses strategy B and player 2 chooses strategy A, then player 1 earns $600 and player 2 earns $100.

a. Write the above game in normal form.

Player 1
Player 2
Strategy	A	B
A	$ , $	$ , $
B	$ , $	$ , $

b. Find each player’s dominant strategy, if it exists.

Player 1's dominant strategy: B   no dominant strategy exists   A  .
Player 2's dominant strategy: B   no dominant strategy exists   A  .

c. Find the Nash equilibrium of this game.

(A,A)   (B,A)   (A,B)   (B,B)

d. Which strategy pair has the highest aggregate payoff?

(B,A)   (A,B)   (B,B)   (A,A)

e. Can the outcome with the highest aggregate payoff be sustained in equilibrium?

No   Yes

Expert Solution

Step 1

Note: Since you have posted a question with multiple subparts, we will solve the first three subparts for you. To get the remaining subparts solved, please repost the complete question and mention the subparts to be solved.

Normal Form:

It is a representation of the game problem in matrix form, where it should be of a square matrix with Strategy and playoff of the players or the top, bottom, left, and right of the players, prisoner's dilemma with cooperating and defect, etc.

Dominated Strategy:

It is the decision made by the players individually with the payoff they get comparing the strategy. The dominating strategy that is the overall higher payoff will be taken by the players.

Nash Equilibrium:

The set of the dominated strategy is the Nash Equilibrium of the game.

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