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):[1]
It is a notion used in the solution concept of subgame perfect Nash equilibrium, a refinement of the Nash equilibrium that eliminates non-credible threats.
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 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 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.