LYCOS RETRIEVER 
Nash Equilibrium: Games
built 655 days ago
A Nash equilibrium, named after John Nash, is a set of strategies, one for each player, such that no player has incentive to unilaterally change her action. Players are in equilibrium if a change in strategies by any one of them would lead that player to earn less than if she remained with her current strategy. For games in which players randomize (mixed strategies), the expected or average payoff must be at least as large as that obtainable by any other strategy.
Source:
Nash equilibrium is one of the central solution concepts for games. The basic idea of a Nash equilibrium is that if each player chooses their part of the Nash equilbrium strategy, then no other player has a reason to deviate to another strategy. A simple example is a coordination game, such as the one in the figure below.
Source:
A similar principle is at work in the famous Prisoner's dilemma game, devised by mathematicians shortly after Nash announced his equilibrium result (4). In this game, two prisoners are each induced to incriminate the other despite the fact that they would both do better if they kept silent. Each acts to further his own interests, but the outcome is in the interests of neither.
Source:
When the 21-year old John Nash wrote his 27-page dissertation outlining his "Nash Equilibrium" for strategic non-cooperative games, the impact was enormous. On the formal side, his existence proof was one of the first applications of Kakutani's fixed-point theorem later employed with so much gusto by Neo-Walrasians everywhere; on the conceptual side, he spawned much of the literature on non-cooperative game theory which has since grown at a prodigious rate - threatening, some claim, to overwhelm much of economics itself.
Source:
What happens if a game has no Nash equilibrium over the space of deterministic strategies? Once again the problem can be alleviated by expanding the strategy space to include randomized strategies. In Section 9.3.3 it was explained that every zero-sum game under Formulation 9.7 has a randomized saddle point on the space of randomized strategies. It was shown by Nash that every nonzero-sum game under Formulation 9.8 has a randomized Nash equilibrium [731]. This is a nice result; ... there are a couple of concerns. There may still exist other admissible equilibria, which means that there is no reliable way to avoid regret unless the players collaborate.
Source:
Abstract : The importance of Nash equilibrium solutions for certain games of imperfect information is illustrated by means of an example. A large number of convergence techniques for the location of Nash equilibria are described and contrasted, for the class of 'convex planar games.
Source:
MORE ABOUT
Games