Question

7. Use the following extensive-form game to answer the questions below.

a. List the feasible strategies for player 1 and player 2.

b. Identify the Nash equilibria to this game.

c. Find the subgame perfect equilibrium.

Short answer

a. The feasible strategies for player 1 will be options A and B.

b. The Nash equilibria are W for player 2, X if player 1 plays 2 and Z if player 1 plays B.

c. The perfect subgame will be the combination B, Z(100,150)

Step-by-step solution

Finding the list of feasible strategies for player 1 and player 2

a.

According to the extensive-form game, the feasible strategies for player 1 will be options A and B, since in both movements he will be able to obtain a payoff.

Again, the feasible strategies for player 2 will be W and X if player 1 plays 2 and Z if player 1 plays B.

Finding the Nash equilibrium\

b.

In an extensive game we can analyze the possible strategies from the last result backwards. Here, we observe which sequence is the most optimal, that is, the backward induction strategy. We also see what happened in the last decision and based on that the penultimate decision is made until the start of the game.

Here, the strategy the player 2 chooses is Z because player 1 chose B. This will be the most optimal strategy and Nash equilibrium since they are the maximum amount that both players can get (100, 150 will be reached).

Similarly, a second Nash equilibrium can be reached in which player2 chooses W if player 1 chooses A generating an equilibrium of (60,120).

Step 3:To find the subgame perfect equilibrium

The perfect balance of a subgame can usually be determined through backward induction of the final results of each game.

The perfect subgame will then be the combination B, Z(100,150) since Player 2 does not have a credible threat to play Y since he would get 0 and it is not Nash equilibrium. Likewise, it would not be in the interest of Player 1 to choose A and obtain a lower profit when player 2 chooses W.