Economics Game Theory Questions
Subgame perfect equilibrium is a solution concept in game theory that applies to extensive form games. It requires that players make optimal decisions not only at the overall game level but also at every subgame within the game.
In an extensive form game, a subgame refers to any part of the game that can be treated as a separate game in itself. It consists of a sequence of actions and decisions that occur after a particular point in the game.
A subgame perfect equilibrium is achieved when players choose strategies that maximize their payoffs at every subgame within the larger game. This means that players make optimal decisions not only at the beginning of the game but also at every subsequent stage, taking into account the strategies chosen by other players.
To determine a subgame perfect equilibrium, we analyze each subgame individually and apply backward induction. Starting from the final stage of the game, we determine the optimal strategy for each player at that stage. Then, we move backward to the previous stage and repeat the process until we reach the initial stage of the game.
By ensuring that players make optimal decisions at every subgame, a subgame perfect equilibrium provides a more refined solution concept than a Nash equilibrium, which only requires players to make optimal decisions at the overall game level. It captures the idea of sequential rationality, where players anticipate and respond to the actions of others throughout the game.