Editing Subgame (section)

{{Short description|Subset of a game; used in game theory}}
{{about|subgames in game theory|subgame as a short video game contained in another| minigame}}

In [[game theory]], a '''subgame''' is any part (a subset) of a game that meets the following criteria (the following terms allude to a game described in [[extensive form game|extensive form]]):<ref>
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|title=Table of Contents for Morrow, J.D.: Game Theory for Political Scientists.
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|accessdate=2008-03-26
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#It has a single initial node that is the only member of that node's [[information set (game theory)|information set]] (i.e. the initial node is in a [[singleton (mathematics)|singleton]] information set).
#If a node is contained in the subgame then so are all of its successors.
#If a node in a particular [[information set (game theory)|information set]] is in the subgame then all members of that information set belong to the subgame.

It is a notion used in the [[solution concept]] of [[subgame perfect equilibrium|subgame perfect Nash equilibrium]], a refinement of the [[Nash equilibrium]] that eliminates [[non-credible threat]]s.

The key feature of a subgame is that it, when seen in isolation, constitutes a game in its own right. When the initial node of a subgame is reached in a larger game, players can concentrate only on that subgame; they can ignore the history of the rest of the game (provided they know [[bayesian game|what subgame they are playing]]). This is the intuition behind the definition given above of a subgame. It must contain an initial node that is a singleton information set since this is a requirement of a game. Otherwise, it would be unclear where the player with first move should start at the beginning of a game (but see [[Bayesian game|nature's choice]]). Even if it is clear in the context of the larger game which node of a non-singleton information set has been reached, players could not ignore the history of the larger game once they reached the initial node of a subgame if subgames cut across information sets. Furthermore, a subgame can be treated as a game in its own right, but it must reflect the strategies available to players in the larger game of which it is a subset. This is the reasoning behind 2 and 3 of the definition. All the strategies (or subsets of strategies) available to a player at a node in a game must be available to that player in the subgame the initial node of which is that node.