# Backward Induction.

Backward induction is a process of reasoning in which one starts from the end of a problem or situation, and then works backwards to the beginning. It is often used in game theory to analyze situations in which players have perfect information (meaning they know all relevant information about the situation, including what other players are thinking and what the possible outcomes of their actions might be).

In game theory, backward induction is often used to find what is called a Nash equilibrium, which is a situation in which no player has an incentive to change their strategy, because doing so would not improve their situation.

To use backward induction to find a Nash equilibrium, one starts by looking at the end of the game, and then works backwards to see what each player would need to do in order to achieve that outcome. For example, in a game of chicken, each player knows that the best outcome for them is if the other player chicken out first. So, if each player knows that the other player is reasoning backwards from the end of the game, they will both chicken out, and the Nash equilibrium is achieved.

### Can backward induction be applied in this game to find a solution?

In game theory, backward induction is a solution concept used to determine the optimal course of action in a sequential game, where the player has perfect information. In a sequential game, each player has a turn to choose their action, and the players can anticipate the actions of their opponents.

In this game, there are two players, Alice and Bob. Alice goes first, and can either cooperate or defect. If Alice defects, then Bob can either cooperate or defect. If Bob defects, then Alice gets 1 point and Bob gets 0 points. If Bob cooperates, then Alice gets 2 points and Bob gets 1 point.

If Alice cooperates, then Bob can either cooperate or defect. If Bob defects, then Alice gets 0 points and Bob gets 2 points. If Bob cooperates, then Alice gets 3 points and Bob gets 1 point.

The game can be represented by the following payoff matrix:

Alice Bob

C C 3,1

C D 2,0

D C 0,2

D D 1,0

Using backward induction, we can see that the optimal course of action for Alice is to defect, since she can get more points by doing so. Bob's optimal course of action is then to cooperate, since he can get more points by doing so.

#### What is backward induction quizlet?

Backward induction is a decision-making process in which one starts with the terminal (end) stage of a problem or process, and then works backwards to the present. It is also sometimes called "reverse induction".

The main idea behind backward induction is that it allows one to focus on the future consequences of present choices, and make decisions accordingly. This can be contrasted with other decision-making processes, such as forward induction, in which one starts with the present and works forwards into the future.

There are a number of different applications of backward induction. One well-known example is in game theory, where it can be used to analyze situations in which two or more people are making decisions that affect each other's payoffs.

Backward induction can also be used in other settings, such as when making investment decisions or when trying to optimize a process. In each case, the goal is to take into account the future consequences of present choices, in order to make the best possible decision. What are the four types of games in game theory? There are four types of games in game theory:

1. Zero-sum games
2. Non-zero-sum games
3. Constant sum games
4. Sequential games What are the two basic types of game in game theory? There are two types of games in game theory: static games and dynamic games. Static games are those in which the player's strategies do not change over time, while dynamic games are those in which player's strategies may change over time. Is game theory math or economics? Game theory is a branch of mathematics that deals with the analysis of strategic interactions between different agents. In game theory, an agent is any decision-making entity, whether it is an individual, a firm, or a government.

Game theory has been used to study a wide variety of phenomena in a variety of fields, such as economics, political science, biology, and psychology. In recent years, game theory has also been used to study problems in a variety of other fields, such as computer science, engineering, and operations research.