Tips for Solving Problems Through Backward Induction

 

Solving problems and finding solutions through applied game theory  tips, techniques, tools, life hacks  tactics, and strategies, 

 

Before we get started, here is a short introduction (including a video)  to help you understand applied game theory. It is written for a child so anyone can understand it. Click below…

 

Q. What is  Backward Induction?

A. Often in problem-solving, we find a solution but aren’t sure how we got there. Backward induction is the process of reasoning backward in time, from the end of a problem or situation, to determine a sequence of optimal actions. It proceeds by first considering the last time a decision might be made and choosing what to do in any situation at that time.

Using this information, one can then determine what to do at the second-to-last time of decision. This process continues backward until one has determined the best action for every possible situation at every point in time. It was first used by Ernst Friedrich Ferdinand Zermelo the German logician and mathematician, in 1913, to prove that chess has pure optimal strategies.

Zermelo’s ideas have had major implications for the foundations of mathematics, for decision science, and in my own work in applied game theory.

Preston Eart a student of Applied Math offered a simple explanation of backward induction on Quora.com

He states as follows;

“If you want to know if you can build a simple bridge with planks of wood across a gap, one way you can show it’s possible is to demonstrate that…

  1. You can stably install the first plank.
  2. The support of the previous plank is sufficient to allow you to stably install the next plank, no matter where in the building process you are.”

This is the essence of the proof by induction. Now to demonstrate this by reversing the process. This is backward induction.

Forward induction is generally an easier and more accurate approach than forward induction however sometimes you just don’t have the information needed.

Backward induction has been used to solve games as long as the field of game theory has existed. John von Neumann and Oskar Morgenstern suggested solving win-lose two-person games by backward induction in their Theory of Games and Economic Behavior (1944), the book which established game theory as a field of study.

 

The Takeaway

Backward induction can be a great tool for solving games, puzzles, and regular challenges in life.

However, one of the great challenges in using backward induction is that the results inferred often fail to predict actual human play. Experimental studies have shown that “rational” behavior (as predicted by game theory) is seldom exhibited in real life.

Author: Lewis Harrison is an author, speaker, seminar leader, and Results-Oriented Life Coach. He has a passion for helping people solve problems, personal growth, self-improvement, and Transmodern Zen

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