Games in Extensive Form: Sequential Decision Making

History is an account, mostly false, of events, mostly unimportant, which are brought about by rulers, mostly knaves, and soldiers, mostly fools.

—Ambrose Bierce

Not the power to remember, but its very opposite, the power to forget, is a necessary condition for our existence.

—Saint Basil

A game in which each player has a single move and the players choose and play their strategies simultaneously are easy to model and write down in matrix form. Many, if not most games involve many moves by each player, with choices made sequentially, with or without knowledge of the moves an opponent has made. We have already met examples of these games in 2 × 2 Nim and Russian Roulette. The sequential moves lead to complicated strategies which, when played against each other, lead to the matrix of the game. That is called putting the game in strategic, or normal form.

4.1 Introduction to Game Trees—Gambit

In this chapter, we consider games in which player decisions are made simultaneously (as in a matrix game) or sequentially (one after the other), or both. These are interchangeably called sequential games, extensive form games, or dynamic games. When moves are made sequentially various questions regarding the information available to the next mover must be answered. Every game in which the players choose simultaneously can be modeled as a sequential game with no information. Consequently, every matrix game can be viewed as a sequential ...

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