# Backward Induction - Explained

What is Backward Induction?

# What is Backward Induction?

Backward induction is a reasoning process that is rooted in game theory. It is a repetitive reasoning process that involves reasoning backward in time. An individual or a player reasons from the end of a problem to determine sequential optimal actions in games. This process of reasoning allows a player to think of the end of a problem and then apply the sequence of happenings to decide what to do at a particular stage. Backward induction has been used as far back as 1944 when John von Neumann and Oskar Morgenstern published a book Theory of Games and Economic Behavior. This process of reasoning was also used by Selten in 1965 in his versions of game.

# How does Backward Induction work?

Backward induction is used by a player to decide on what move to make at a particular stage by a process of reasoning backward in time. The player considers the end of a problem and makes current decisions based on this. According to rational behavior highlighted in this theory sometimes reflect in real life but the theory does not precisely predict humans. In this theory, a player that makes the last move in a game uses an optimal strategy determined by this theory. Thereafter, the action of the player before the last one is determined by the last players action. The gaming process moves backward until the best optimal action for each subgame is determined.

# Example of Backward Induction

This illustration is important for a better understanding of how a backward induction works. Player X plays first in the game and he needs to decide whether to take the stash worth \$4 or pass it. If Player X takes it, the \$4 will be shared between him and Player Y (\$2 each), if he passes it, Player X will also need to decide whether to take or pass the stash. If Player Y passes, he gets an extra amount added to the existing \$2 while Player X gets no amount. However, if both players cooperate and keeps passing, they receive an equal payoff at the end of the game, but the reverse is the case if they do not cooperate.

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