Economics Game Theory Questions Long
Backward induction is a strategic decision-making process used in dynamic games, particularly in sequential games, where players take turns to make decisions. It involves reasoning backward from the end of the game to determine the optimal strategy for each player at each stage of the game.
In dynamic games, players make decisions sequentially, and the outcome of each player's decision depends on the decisions made by previous players. Backward induction helps players anticipate the actions of other players and make rational decisions based on their expectations.
The process of backward induction starts from the last stage of the game and moves backward to the first stage. At each stage, players consider the possible actions of the subsequent players and choose their strategies accordingly. By reasoning backward, players can determine the optimal strategy that maximizes their payoffs at each stage.
To illustrate the concept of backward induction, let's consider a simple example known as the "Centipede Game." In this game, two players take turns deciding whether to continue or stop. The game starts with a pot of money, and at each turn, the pot doubles. If a player decides to stop, the game ends, and the players split the money in the pot. However, if a player decides to continue, the other player has the option to stop at the next turn and take the entire pot.
Using backward induction, we start from the last stage of the game. In this case, it is the second-to-last turn. The player who has the option to stop at this stage realizes that if they continue, the other player will stop at the next turn and take the entire pot. Therefore, the rational decision for the player at this stage is to stop and take their share of the pot.
Moving backward to the first stage, the player who has the first turn knows that if they continue, the other player will stop at the second-to-last turn. Hence, the rational decision for the first player is to continue and double the pot.
By reasoning backward in this manner, we can determine that the optimal strategy for both players is for the first player to continue at the first turn, and the second player to stop at the second-to-last turn. This strategy maximizes the payoffs for both players.
Backward induction is a powerful tool in game theory as it allows players to anticipate the actions of others and make rational decisions based on their expectations. It helps in determining the equilibrium of the game, where no player has an incentive to deviate from their chosen strategy. However, it is important to note that backward induction assumes rationality and perfect information, which may not always hold in real-world situations.