Finding the Nash equilibrium often represents a thorny problem, with this article we try to provide a quick tutorial to calculate the Nash equilibrium in any matrix of any size, but using a 2X2 matrix as an example.

(Dominant strategy method) – summary (tutorial):

1) Check each column to find the one where player 1 has maximum payout
2) Check if the choice of 1 tends to always be the same, whatever the choice of player 2 (dominant strategy)
3) Repeat for the same player the same procedure
4) The Nash equilibrium is reached where the dominant strategies intersect

(Thumb method) – summary (tutorial):

1) Identify an opponent’s choice and check if the player would have an incentive to change choice
2) If he has no interest, circle the payoff; if yes check another choice of the opponent
3) Repeat the choice for all the choices of all the players
4) The Nash equilibrium occurs when 2 payoffs are circled in the same cell (keep in mind that there may be more Nash equilibria)

Let’s look at an example to complete the tutorial on how to calculate the Nash equilibrium:

 

---

Example on how to calculate the Nash equilibrium (video guide)

A tutorial to understand how to calculate the short but explanatory Nash equilibrium is the one contained in the following video: