Editing Nash equilibrium (section)

=== Where the conditions are not met ===
Examples of [[game theory]] problems in which these conditions are not met:
# The first condition is not met if the game does not correctly describe the quantities a player wishes to maximize. In this case there is no particular reason for that player to adopt an equilibrium strategy. For instance, the prisoner's dilemma is not a dilemma if either player is happy to be jailed indefinitely.
# Intentional or accidental imperfection in execution. For example, a computer capable of flawless logical play facing a second flawless computer will result in equilibrium. Introduction of imperfection will lead to its disruption either through loss to the player who makes the mistake, or through negation of the [[common knowledge (logic)|common knowledge]] criterion leading to possible victory for the player. (An example would be a player suddenly putting the car into reverse in the [[game of chicken]], ensuring a no-loss no-win scenario).
# In many cases, the third condition is not met because, even though the equilibrium must exist, it is unknown due to the complexity of the game, for instance in [[Chinese chess]].<ref>T. L. Turocy, B. Von Stengel, ''[http://www.cdam.lse.ac.uk/Reports/Files/cdam-2001-09.pdf Game Theory]'', copyright 2001, Texas A&M University,  London School of Economics, pages 141-144. {{Citation needed span|text=Nash proved that a perfect NE exists for this type of finite [[extensive form game]]|date=April 2010}} – it can be represented as a strategy complying with his original conditions for a game with a NE. Such games may not have unique NE, but at least one of the many equilibrium strategies would be played by hypothetical players having perfect knowledge of all {{Citation needed span|text=10<sup>150</sup> [[game-tree complexity|game trees]]|date=April 2010}}.</ref> Or, if known, it may not be known to all players, as when playing [[tic-tac-toe]] with a small child who desperately wants to win (meeting the other criteria).
# The criterion of common knowledge may not be met even if all players do, in fact, meet all the other criteria. Players wrongly distrusting each other's rationality may adopt counter-strategies to expected irrational play on their opponents’ behalf. This is a major consideration in "[[Game of chicken|chicken]]" or an [[arms race]], for example.