3.2 Nash Equilibria in Two-Player Matrix Games
For a two-player matrix game, we can set up a matrix with each element containing a reward for each joint action pair. Then the reward function 
A two-player matrix game is called a zero-sum game if the two player are fully competitive. In this way, we have 
general-sum matrix game refers to all types of matrix games. In a general-sum matrix game, the NE is no longer unique and the game might have multiple NEs.
For a two-player matrix game, we define 
An NE for a two-player matrix game is the strategy pair 
where 
Given that each player has two actions in the game, we can define a two-player two-action general-sum game as
where 
strict NE in pure strategies if
where 