In game theory, a non-cooperative game is a type of game in which players make decisions independently, without any communication or agreement. Each player chooses their actions based solely on their own interests and without considering the impact of their decisions on other players.

Non-cooperative games are often used to model situations where there is competition or conflict between players. In these types of games, each player is trying to maximize their own payoff or minimize their losses, regardless of the strategies chosen by other players.

**Types of Non-Cooperative Games:**

- Simultaneous Games: In simultaneous games, all players choose their strategies at the same time without observing other players’ choices.
- Sequential Games: In sequential games, one player chooses his/her strategy first and the other player(s) observe that strategy before making their own decision.

**Nash Equilibrium:**

In non-cooperative games, a Nash equilibrium is a set of strategies that each player chooses which are best responses to each other’s strategies. No player has an incentive to change his/her strategy given the strategies chosen by others. Nash equilibrium is considered as a very important concept in game theory and is widely used in various fields like economics, political science, biology etc.

__Examples:__

One classic example of a non-cooperative game is the Prisoner’s Dilemma. In this scenario, two criminals are arrested and separated from each other. They both have to decide whether to confess or stay silent.

If both confess, they will get 5 years each in prison. If one stays silent and the other confesses, the one who confesses will get only 1 year while the one who stays silent will get 10 years. If both stay silent, they will both get only 2 years.

### The Bottom Line

Non-cooperative games can be seen as a way to model situations where players act independently and competitively. These types of games can help us understand how different players make decisions based on their own interests and how they might react to the strategies chosen by other players. Nash equilibrium is a key concept in non-cooperative games and can help us predict the outcomes of these types of games.