This video explains what the extensive form is. We start by learning how to build a game tree to analyse games, and then use a couple of examples to see how to use it.
In game theory, the extensive form is a way of describing a game using a game tree. It’s simply a diagram that shows that choices are made at different points in time (corresponding to each node). The payoffs are represented at the end of each branch. Since the extensive form represents decisions at different moments, it’s usually used to describe sequential games, while simultaneous games are described using the strategic form. Since sequential games imply making decisions at different moments for each player, information is perfect since each player can see the decision taken by the previous player, complete and the rules of the game and each player’s payoffs are common knowledge.
A good example of a sequential game described with the extensive form is when considering collusion agreements. Two firms share the market, colluding and maintaining high prices. Each firm can decide to stop colluding and start a price war, in order to increase their market share, even force the other to quit the market. It’s easy to see that collude-collude is both the Nash equilibrium and a Pareto optimum situation. This result may change when considering repeated games.
It’s worth mentioning that the extensive form can be used also to describe simultaneous games, by using information sets. These information sets, usually represented by a dashed line uniting two nodes or by encircling them, mean that the player does not know in which node he is, which implies imperfect information, like when using the strategic form.
Learn more by reading the dictionary entry.