Pure Strategy Nash Equilibrium

The game is in equilibrium when players chooses best responses to the other's strategy.

Example

Consider the game

Ben


Anna
Help Leave
Help 3, 2 0, 0
Leave 0, 0 2, 1

Anna can Help or Leave the village. Ben can also either Help or Leave.

In equilibrium:

  • Anna plays a best response to Ben's strategy.
  • Ben plays a best response to Anna's strategy.

Here, they reach an equilibrium when they take the same action.

Ben


Anna
Help Leave
Help 2, 1 0, 0
Leave 0, 0 3, 2

(Help, Help) is an equilibrium. (Leave, Leave) is an equilibrium too!

Question

The payoff matrix is

Ben


Anna
Help Leave
Help 30, -95 -2, 6
Leave -47, -83 -9, 52

What is the equilibrium(s) of the game above?

The equilibrium is (Help, Leave)