Question

Which of the following statements is CORRECT for Game A and Game B?

Game A: Mary wants to watch a movie and John is interested in watching a football match. Both wish to be together. The payoff matrix is:

Game B: The Prisoner's dilemma problem is shown below:

• A. In Game A. (Movic, Football) and (Football, Movie) represent Nash equilibrium. In Game B, (Do not confess, Do not confess) is the Nash Equilibrium.
• B. In Game B, (Confess, Confess) is not a Nash equilibrium but in Game A, both (Movie, Football) and (Football, Movie) represent Nash equilibrium.
• C. In Game B, the Nash equilibrium is (Do not confess, Do not confess).
• D. In Game A, both (Movic, Movie) and (Football, Football) represent Nash equilibrium. In Game B, the Nash equilibrium is (Confess, Confess).

Answer 1

The Correct Option is D

Let's analyze the payoff matrices for both Game A and Game B to determine the Nash equilibrium points.

Game A:

	Movie	Football
Movie	(2,1)	(0,0)
Football	(0,0)	(1,2)

In Game A, the Nash equilibrium is where neither player can improve their payoff by unilaterally changing their strategy. The two Nash equilibria are:

• (Movie, Movie): Here, Mary and John both watch a movie, and their payoffs are (2, 1).
• (Football, Football): Here, both Mary and John watch football, and their payoffs are (1, 2).

Both these strategies satisfy the Nash equilibrium condition as neither player has anything to gain by changing only their own strategy unilaterally.

Game B: The Prisoner's Dilemma problem

	Do not confess	Confess
Do not confess	(-1,-1)	(-9,0)
Confess	(0,-9)	(-5,-5)

In Game B, the Nash equilibrium is (Confess, Confess) where both convicts choose to confess. This is because neither player gains from switching to "Do not confess" while the other confesses. They both get a higher penalty if one switches unilaterally.

Therefore, in conclusion:

• In Game A, both (Movie, Movie) and (Football, Football) represent Nash equilibria.
• In Game B, the Nash equilibrium is (Confess, Confess).