**Nash equilibrium perfect by subgames** ^{[1]} ( eng. Subgame perfect Nash equilibrium , SPNE) - the concept of a solution in game theory , refining Nash equilibrium for games in a detailed form .

Equivalence perfect by subgroups | |
---|---|

The concept of solution in game theory | |

Related decision sets | |

Supersets | Nash equilibrium |

Subsets | Evolutionarily stable strategy |

Data | |

Authorship | Reinhard Zelten |

Application | Games in expanded form |

A set of players' strategies is called an equilibrium perfect for subgroups if its restriction to any subgame of this game is Nash equilibrium in it. Intuitively, this means that the actions of the parties in a game will be the same, regardless of whether it is played out separately or is part of a more general game.

Equilibrium perfect in subgames allows you to weed out Nash equilibria based on inaccurate threats from players.

A common solution method is reverse induction , in which the optimization of player moves begins at the end of the game. This method does not work if there are no subgames in the game, as well as for repeated games with an infinite horizon.

The game is in expanded form

Nash equilibrium imperfect subgames

Equivalence perfect by subgroups

## Content

## See also

- Non-cooperative game
- Nash equilibrium

## Literature

- Vasin A. A., Morozov V. V. Game Theory and Models of Mathematical Economics. - M., 2005.
*Petrosyan L. A. , Zenkevich N. A., Semina E. A.*Game Theory: Textbook. allowance for un-com. - M .: Higher. shk., Book House "University", 1998. - p. 304. - ISBN 5-06-001005-8 , 5-8013-0007-4.- Pechersky S. L., Belyaeva A. A. Game Theory for Economists. Introductory course. Tutorial. - SPb .: Ed. European University at St. Petersburg, 2001.

## Notes

- Russian-English dictionary of mathematical terms. - American Mathematical Society. E.D. Lowoter. 1990

## Links

- An example of a game in expanded form with imperfect information
- Java applet for finding the perfect subgame balance with gametheory.net.
- Example of equilibrium perfect by subgroups (inaccessible link from 13-05-2013 [2265 days] -
*history*)