Backward induction is a process of reasoning in which one works backwards in time to infer what a player will do in the present. It is important in economics because it can be used to predict how economic agents will behave in different situations.
For example, consider a firm that is trying to decide whether to invest in a new project. The firm will use backward induction to reason about how much money it will make from the project over time. If the firm expects to make more money from the project than it would without investing, then it will invest; if not, it will not invest. This process of reasoning allows firms to make decisions that are in their best interests, and as a result, helps to ensure that resources are allocated efficiently in the economy.
Backward induction can also be used to predict how consumers will behave. For example, consider a consumer who is trying to decide whether to buy a new car or keep their old car. The consumer will use backward induction to reason about how much money they will save by buying a new car. If the consumer expects to save more money by buying a new car, then they will buy; if not, they will keep their old car. This process of reasoning allows consumers to make decisions that are in their best interests, and as a result, helps to ensure that resources are allocated efficiently in the economy.
Overall, backward induction is a powerful tool that can be used to predict how economic agents will behave in different situations. It is important in economics because it helps to ensure that resources are allocated efficiently in the economy.