Backward Induction Game Theory Explained


Have you ever played a video game, or perhaps a game of chess, with a friend? If you were competing against them, did you attempt to predict what their next move might be? One way to create a potential outcome is to analyze what your opponent hopes to accomplish and then figure out what moves will be required for your opponent to get there.

That is the concept behind the backward induction game theory. Instead of trying to predict opponent moves based on forward-thinking responsiveness, you attempt to predict what will happen by identifying the entire chain of decisions that are needed to achieve victory.

By identifying the decision-making path, the next moves can be predicted, which puts you into the driver’s seat to win since you’ve got an idea of what your opponent is thinking about.

It is an idea that was first proposed in 1944 by John von Neumann and Oskar Morgenstern.

Issues with the Backward Induction Game Theory

The primary issue with the backward induction game theory is that it only applies to one player in the game. The last player to take a turn in a two-player game is where the moves can be anticipated because their moves are responsive to the moves of the first player. For the theory to work, the first player must make several assumptions about the second player.

  • The game must be played logically. The first player must assume that the second player is always going to choose the most logical course of action during their turn.
  • There must be expertise. If the second player doesn’t know how to play the game or has only played it a handful of times, then their lack of expertise can lead to a level of unpredictability that can differ from what a logical outcome should be.
  • Players must be competitive. The first player must assume that the second player is attempting to win the game. If someone is just playing for fun and doesn’t care about the outcome, then the theory cannot be implemented because there is no authentic predictor for the overall outcome.
  • The other player has a similar experience. The first player is judging the proposed steps of the second player based on their experiences with the game. If the other player sees the game differently, then they will play it differently, and that makes it difficult for this theory to be implemented.

Not every game is suited to the backward induction game theory. Games of chance, in particular, are designed to be unpredictable. If you were to play Monopoly with someone else, there is no telling who might land on Boardwalk or what they might do with it. Predicting a path toward victory from a backwards induction perspective would therefore be a waste of time.

The Issue Caused by Backward Induction Game Theory

Imagine that a person is told that something bad will happen to them next week at some point, between the days of Monday and Friday. To avoid having something bad happen, the individual attempts to deduce what day this event will occur.

Using backward induction game theory, the individual surmises that it cannot happen on Friday. That is because if nothing had happened by Thursday evening, they would know the event would happen on Friday and it could be avoided.

With Friday ruled out, the individual now determines that Thursday cannot be the day something bad happens either. That’s because if nothing happened by the end of the day on Wednesday, it would be known that Thursday would be the day because Friday has already been ruled out.

Using that form of deductive reasoning, every day can be eliminated. The individual comes to the conclusion that nothing bad is actually going to happen to them. In reality, an eviction notice has already been sent in the mail with a tracking code and is scheduled to arrive on Tuesday, with a late delivery estimate of Friday.

Backward induction game theory can lead to false conclusions more often than not. It is an exclusionary, not inclusionary, thinking process. The second player can decide to gamble, taking a risk they normally wouldn’t take, and that can completely change the predicted outcome for the first player without any warning.

That’s why this theory, which is also referred to as “retrograde analysis,” could be applied to the field of economics or other areas of society, but is not. Although it offers the potential of success, there is a greater potential of failure when it is applied.