Backward induction concept: How can it help us in real-life decisions?

In the current post, I will write about a concept from game theory that could make a decision-making process more manageable. Game theory, in general, is the study of mathematical models that model interaction between rational agents. This game theory concept is also applied in decision theory and is entitled backward induction. Backward induction is a concept often used to solve sequential games, where players make decisions one after another. It involves working backward from the end of a game to its beginning, considering each player's optimal choices at each stage. This technique helps players determine the best strategies by considering the potential outcomes of different decisions.

The first to introduce the concept was Arthur Cayley in 1887, who discovered the method while trying to solve the infamous Commissioner Problem.  John von Neumann and Oskar Morgenstern, the game theory pioneers, introduced the backward induction concept as a game-solving process in their book Theory of Games and Economic Behavior (1944).  There have been many academic works done in that field since then. Kreps and Wilson did the first and more solid definition of this concept in terms of game theory in 1982.

The concept of backward induction is a fundamental idea in game theory and decision-making, and its development can be attributed to multiple researchers over time. While it's challenging to pinpoint a single individual as the "first" to introduce the concept, its foundations have been built upon the works of various mathematicians, economists, and scholars.

How can the concept help in everyday decision-making? I will try to answer that in detail.

Remember that real-life decisions can be more complex and uncertain than simplified examples and unexpected factors might arise. However, the backward induction approach can provide a structured way to think about decisions and their potential consequences in a strategic manner.

Here's how backward induction can be applied as a decision-making tool:

1. Define the End Goal: Clearly identify your ultimate objective or desired outcome. This could be achieving a career milestone, maximizing profits in a business venture, or any other goal involving a series of decisions.
2. Identify Intermediate Steps: Break down the journey toward your goal into intermediate steps or stages. Consider what needs to be accomplished at each stage to move closer to your end goal.
3. Evaluate Options at Each Stage: Consider each intermediate stage's available options or choices. Analyze the potential outcomes of each choice, including the impact on future stages and the overall goal.
4. Consider Consequences: Analyze the consequences of each option on future decisions and outcomes. Think about how each choice will influence subsequent choices and whether it will move you closer to or farther from your ultimate goal.
5. Work Backward: Start from the final stage and work backward through the stages, considering the optimal choices at each step. This involves considering what decision you would make if you were at the last stage, given the best choices made in the subsequent stages.
6. Choose the Best Path: Select the option that leads to the most favorable outcomes at every stage, ultimately aligning with your end goal.

Here's the first example of how it might be used:

Example: Job Offer Decision

Imagine you are a recent college graduate who has received multiple job offers. You need to decide which job to accept. Each job has different salary packages, work environments, and potential career paths. You decide to use the backward induction approach.

1. Identify the End Point: Start by clearly defining your ultimate objective or desired outcome. This could be a long-term goal, a project completion, a career milestone, or any decision-making situation with multiple steps. For example, what do you ultimately want to achieve in your career? This could be becoming a manager, working in a specific industry, or starting your own business.
2. Work Backward: Think about the path that will best lead you to your long-term goals. Consider the potential career progression at each job, the skills you will acquire, and the network you will build.
3. Consider Intermediate Goals: Break down your long-term goal into intermediate goals. For example, if your goal is to become a manager, you might need to first gain experience in a certain role and develop specific skills.
4. Evaluate Job Offers: Compare the job offers based on how well they align with your intermediate and long-term goals. Consider factors like salary, benefits, location, opportunities for growth, and alignment with your values.
5. Select the Best Option: Choose the job offer that best aligns with your goals and offers the most promising path toward achieving them.

By using backward induction, you've thoughtfully analyzed each job offer in the context of your long-term objectives. This approach helps you make a decision that aligns with your aspirations and maximizes your chances of success.

Here's a simplified second example to illustrate these steps:

Example: Vacation Planning

1. Define the End Goal: Plan a memorable vacation.

2. Identify Intermediate Steps: Choose a destination, book accommodations, plan activities, pack, and travel.

3. List Available Options: Destination A, Destination B, etc. Different accommodations, activity options, etc.

4. Analyze Potential Outcomes: Consider costs, available attractions, weather, convenience, etc.

5. Consider Interactions: Booking accommodations might depend on the chosen destination.

6. Determine Optimal Choices: Choose a destination that aligns with your preferences and offers the best experience.

7. Evaluate Alignment: Ensure that the chosen destination and planned activities align with your vacation goal.

8. Select the Best Path: Make decisions that lead to a well-planned vacation.

9. Contingency Planning: Plan for unexpected weather or activity cancellations.

10. Execute and Monitor: Book accommodations, plan activities, and track progress.

11. Adapt and Update: Adjust plans if weather conditions change or new activities become available.

In conclusion, backward induction is a valuable concept in game theory and decision-making that involves working backward through a sequence of decisions or stages to determine optimal strategies or outcomes. It is a powerful tool for analyzing strategic interactions in various contexts, from simple games to complex real-life situations. In essence, backward induction provides a structured and forward-thinking approach to decision-making, allowing individuals to make rational choices by considering the long-term implications of their actions.

 The pictures in this post were taken from Unsplash.