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 of leave a village attacked by zombies.

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

Consider the following payoff matrix:

Ben


Anna
Help Leave
Help 69, 27 -1, -39
Leave 95, -64 -59, -76

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

The equilibrium is (Leave, Help)