Subgame Perfect Nash Equilibrium

Question 1

What do we do when we find the SPNE?

Answer 1

Eliminate non-credible threats.

It means we find the more likely of the Nash equilibria.

Question 2

What is a subgame?

Answer 2

A game within a game. whenever a player has a decision to make, we can consider that as a game and find the NE of that game.

Question 3

SPNE characteristics

Answer 3

They don’t need to be unique, and we find it via backwards induction.

Question 4

Backwards Induction Process

Answer 4

Find the equilibrium for each subgame, which will be the outcome with the highest utility.

Drop the subgame with the lower utility.

Repeat until we find the subgame with the highest utility.

Question 5

Backwards Induction Maths

Answer 5

Player one chooses action a1 E A1.

Player two chooses their action given player one’s choice: a2 E A2(a1).

Max P2 (a1, a2)
a2 E A2

Solution to problem is player 2’s best response function a2 = R2(a1). Player one knows if he chooses a1 E A1, then player 2 will do this.