Chapter 7 - Extensive form games and backwards induction. Recap. In the previous chapter. Let us represent this as a normal form game. We use backward induction to identify the Nash equilibria. The dominant strategy for the follower is: Class website for my third year Game Theory course. This lecture introduces backward induction, the most common solution algorithm for extensive form games. Takeaway Points. A subgame perfect equilibrium is an equilibrium in which all actions are Nash equilibria for all subgames.; We can find such equilibria by starting using backward induction, which instructs us to start at the last action and work our way progressively backward from there.
Backward induction in game theory is an iterative process of reasoning backward in time, from the end of a problem or situation, to solve finite extensive form and sequential games, and infer a sequence of optimal actions. Namespaces Article Talk. But if B passes, A now gets to decide whether to take or pass, and so on. Economics Microeconomics Macroeconomics Behavioral Economics. In chess it is called retrograde analysis. The initial node has no predecessor.
That is, by anticipating what the last player will do in each situation, it is possible to determine what the second-to-last player will do, and so on. Suppose a prisoner is told that she will be hanged sometime between Monday and Friday of next week. Retrieved In other words, rationality should be common knowledge. The result is an equilibrium found by backward induction of Player 1 choosing "right" and Player 2 choosing "up. The intuition is that if one expects to work in a job for a long time, this makes it more valuable to be picky about what job to accept.
Backward induction has been used to solve games since John von Neumann and Oskar Morgenstern established game theory as an academic subject when they published their book, Theory of Games and Economic Behavior in Irrational players may actually end up obtaining higher payoffs than predicted by backward induction, as illustrated in the centipede game. The game is also sequential, so Player 1 makes the first decision left or right and Player 2 makes its decision after Player 1 up or down. Consider two individuals: a seller and a buyer. At either information set we have two choices, four in all. Consider the actions of the second player given any arbitrary proposal by the first player that gives the second player more than zero.