Game Theory: The Mathematics of Game Theory – Part 4

The Mathematics of The Nash Equilibrium

This will be the final part of the mathematics of game theory, completing the four-part series.

Let’s return to the beginning when I wrote the introduction to this section on game theory in mathematics. We discussed the Nash Equilibria, which describes the set of strategies that are the best response to strategies chosen by other players. As a result of the Nash Equilibria, if every player chooses the optimal strategy, no other player should change strategy from their optimal strategy. This scenario is referred to as pure Nash Equilibrium.

Photo by Mattia Bericchia on Unsplash

But are all players rational? We see in poker, psychology is a large part of the game. Mathematics can’t explain everything alone. A player could misplay a few hands, and act as though they lack confidence in their decisions. Only to then reveal they are an incredibly skilled player and go on to win many hands.

The existence of Nash Equilibria in games depends on the characteristics introduced in the game theory introduction.

· Number of Players

· Strategies Per Player

· Number of Nash Equilibria

· A Sequential Game

· Perfect Information

· Constant Sum Game

· Random Moves By Nature

Regardless of all these characteristics, the best way to represent a game from every player's point of view is with a payoff matrix. I will explain how to construct this for any game you come across.