Nash equilibrium for big data [closed]

1. When would there be no Nash equilibrium?
2. Is it possible to have no Nash equilibrium game theory?
3. Does Nash equilibrium always exist in finite games?
4. Is the prisoner dilemma a Nash equilibrium?

When would there be no Nash equilibrium?

Nash equilibria need not exist if the set of choices is infinite and non-compact. An example is a game where two players simultaneously name a number and the player naming the larger number wins.

Is it possible to have no Nash equilibrium game theory?

John Nash's notion of equilibrium is ubiquitous in economic theory, but a new study shows that it is often impossible to reach efficiently. All games have a Nash equilibrium.

Does Nash equilibrium always exist in finite games?

Theorem (Nash) Every finite game has a mixed strategy Nash equilibrium.

Is the prisoner dilemma a Nash equilibrium?

The likely outcome for a prisoner's dilemma is that both players defect (i.e., behave selfishly), leading to suboptimal outcomes for both. This is also the Nash Equilibrium, a decision-making theorem within game theory that states a player can achieve the desired outcome by not deviating from their initial strategy.