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Chapter 14: Problem 2

How are decision trees used to analyze sequential games?

Short Answer

Expert verified
Decision trees are used to analyze sequential games by providing a graphical representation of the possible decision paths and their resulting outcomes. Each node in the tree represents a decision, and each branch represents an outcome. This visual approach allows for a systematic way to navigate the sequence of decisions and outcomes in the game. Ultimately, it aids in the identification of optimal strategies based on the expected utility of each decision path.

Step by step solution

01

Understand the concept of sequential games

Sequential games are a type of game theory where the order of play matters. One player makes a decision, and then the other player(s) make their decision(s) in turn, knowing what the previous player(s)' decisions were. The representative example is chess. The entire history of preceding moves is known to both players, which influences their future decisions.
02

Understand the concept of decision trees

A decision tree is a graphical representation of all the possible decision paths to be made given a set of alternatives. It illustrates sequences of decisions and chance outcomes in the form of branches, where each decision point, known as node, leads to an outcome or another decision. In the context of sequential games, decision trees provide a systematic way of considering all possible outcomes of a game, going through each decision sequentially.
03

Apply decision trees to sequential games

To use a decision tree in analysing a sequential game: First, specify the order of moves by the players. Draw a node for each decision to be made. Arrows lead from each node representing each possible decision, and end at either another node or at an outcome. Players' payoffs are written at the end of each branch. This graphical display can then be used to compute and compare the expected utility of each decision path, allowing players to identify the best strategies.

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Most popular questions from this chapter

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