The concept of Nash equilibrium is commonly discussed alongside game theory. It is the concept in which all players are not cooperating with one another but each is able to come up with the best possible decision. How? They do this by understanding and knowing the decisions of the rest of the players. The only catch here is that Nash equilibrium is only achieved when the rest of the players do not change their decision. Once each player has nothing to gain by changing his or her own strategy then, the strategies and the corresponding payoffs are said to properly constitute Nash equilibrium.
This concept was first introduced in the late 19th century when Cournot penned his theory on oligopoly. Cournot believes that a firm chooses the output that would maximize his profits. This choice is decided based on the choice and corresponding payoffs of other firms. This in itself is an example of Nash equilibrium. But as more minds delved into this concept, different types of Nash equilibrium were formed. The one referred to by Cournot constitute a pure strategy Nash equilibrium. The highly distinguished von Neumann, on the other hand, introduced the mixed strategy Nash equilibrium wherein players tend to choose over a set of possible decisions. They, in turn, would attempt to identify the probability of each from happening.
While successful in its early phases, many analysts believe that the solution concept of Nash equilibrium is not without faults. They believe that this concept is not credible. It is rare in any situation for all the players to have perfect information of one another which makes the concept unreliable. At the same time, the concept failed to address the situation if the game is repeated. What would happen to the decisions and strategies of the players?
The Wonderful World of Algorithms 