# Backward Induction

## DEFINITION of 'Backward Induction'

The process of deducing backwards from the end of a problem or scenario to infer a sequence of optimal actions in game theory. Backward induction starts at the final step in a game, and by anticipating what the last player in a two-player game will do at that point, determines what moves likely lead to it. The results inferred from backward induction often do not hold up in real life. Backward induction was first mentioned by game theory inventors John von Neumann and Oskar Morgenstern in 1944.

## BREAKING DOWN 'Backward Induction'

There are several problems associated with the results obtained from backward induction. Firstly, it may not reflect how players in a game actually play, as the actual pattern of play may differ from the pattern deduced by backward induction. Secondly, people who play naively or illogically may actually end up obtaining higher payoffs or utilities than the payoffs predicted by backward induction in well-known game theory games such as Centipede and Traveler’s Dilemma.

For example, the Centipede Game is an extensive-form game in which two players alternately get a chance to take the larger share of a stash of money from two piles of money (contributed by a third party). Each time the money passes across the table, the quantity doubles. The game concludes as soon as a player takes the stash, with that player getting the larger portion and the other player getting the smaller portion. A total of 99 rounds are played, and if both players always choose to pass (rather than take), they each receive an equal payoff of \$50 at the end of the game.

Backward induction predicts that the first player will choose to take on the very first move. However, in experimental studies, only a very small percentage of subjects chose to take on the first move, which is intuitively not surprising given the tiny starting payoff when compared with the much larger payoffs as the game progresses.