Final answer:
A Subgame is a portion of a larger game that can be analyzed as a complete game on its own, starting at a specific decision node. Subgame Perfect Equilibrium is a strategy that is Nash Equilibrium for the entire game and all possible subgames, meaning it is the optimal strategy for every stage of the game.
Step-by-step explanation:
Subgame refers to a portion of a larger game that can be analyzed independently as a complete game in itself. It starts at a particular decision node and includes all the future actions and their respective payoffs from that node onward, assuming that the game has reached that point and ignoring all previous actions. A subgame must contain all the future moves that can follow from its starting node, following the same rules as the original game. A standard example of a subgame can be found in chess, where after a series of moves, the game can be analyzed from the current position without considering the previous plays.
Subgame Perfect Equilibrium (SPE) is a refinement of Nash Equilibrium used in dynamic games. An equilibrium is subgame perfect if it represents a Nash Equilibrium of every subgame of the original game. This means that the strategy choices are optimal given the choices of others, not only for the game as a whole but for every subgame that may occur. A commonly used illustration of SPE is in the study of bargaining problems and sequential games where players' moves are observed by all players.