subgame

Subgame is a concept in game theory referring to a portion of an extensive-form game that can be analyzed as an independent game from that point forward. A subgame begins at a decision node and includes all subsequent moves and outcomes, forming a complete, self-contained extensive-form game. The boundary of a subgame cannot cut through any information set, and the starting node must belong to a single information set (i.e., be a singleton) so that the subgame has well-defined moves for the players who act within it.

Subgames enable iterative reasoning through backward induction and the definition of subgame-perfect equilibrium. A strategy profile is a subgame-perfect equilibrium if it constitutes a Nash equilibrium in every subgame of the original game. This requirement rules out non-credible threats that could arise in off-path branches.

Not every part of a game is a subgame. The boundary must respect information structure, so if some information sets cross the boundary between inside and outside the candidate subgame, it is not a subgame. Subgames can be nested; the overall game is itself a trivial subgame of itself, and smaller subgames can be analyzed inside larger ones.

In practice, identifying subgames allows the use of backward induction and modular analysis, simplifies computations, and clarifies strategy credibility. Subgame analysis is fundamental in dynamic games, repeated games, and in mechanism design and auction theory under sequential participation.