Economics Game Theory Questions Long
Subgame perfection is a refinement concept in game theory that helps identify the most credible and realistic outcomes in sequential games. It is a solution concept that requires players to make rational decisions not only at the overall game level but also at each subgame within the larger game.
To understand subgame perfection, it is important to first grasp the concept of a subgame. A subgame is a smaller game that arises within a larger sequential game when a player has to make a decision at a particular point in the game. It represents a subset of the original game that starts at a specific decision node and includes all subsequent moves and outcomes.
In a sequential game, players make decisions in a specific order, and each player's decision depends on the actions taken by the previous players. Subgame perfection focuses on identifying strategies that are optimal not only in the overall game but also in each subgame.
A strategy is considered subgame perfect if it represents a credible and rational plan of action for each player at every subgame. This means that players must not only consider their immediate payoffs but also take into account the potential future consequences of their actions.
To determine subgame perfection, we use a backward induction approach. Starting from the final subgame, we analyze the optimal strategies for each player. Then, we move backward to the previous subgame and repeat the process until we reach the initial decision node.
The key idea behind subgame perfection is that players should not make any non-credible threats or promises. A non-credible threat is a threat that a player would not actually carry out, while a non-credible promise is a promise that a player would not fulfill. By eliminating non-credible strategies, subgame perfection helps identify the most realistic and credible outcomes in a game.
Subgame perfection is particularly useful in analyzing games with multiple stages or rounds, such as repeated games or dynamic games. It helps us understand how players strategically plan their actions over time, taking into account the potential consequences of their decisions.
In summary, subgame perfection is a refinement concept in game theory that focuses on identifying strategies that are optimal not only in the overall game but also in each subgame. It helps eliminate non-credible threats and promises, leading to more realistic and credible outcomes in sequential games.