7 - Extensive Form Games

Summary

Because all players choose their strategies simultaneously, normal form representations of games are static. Many applications in political science, however, involve players choosing strategies sequentially. Although it is possible to model these situations as games in the normal form, it is often easier and more satisfying to use the extensive form, which treats time explicitly.

To motivate the extensive form, consider the following application. A is a colony controlled by B. Country B generates revenue from control of A's oil fields and from direct taxes on A's residents.

In the first stage, A decides whether to Revolt or Consent to the status quo. If A revolts, B decides whether to Grant independence or to Suppress the revolution. If B suppresses, the situation escalates into a war. In the event of war, A wins with probability p. At stake is control of the lucrative oil field, which generates a payoff of 4 to the side that controls it.

Starting a revolution costs A one unit if B does not suppress. Suppression by B costs each side 6 units. If A does not revolt, B can continue to Tax A's residents at 2 units or it can Eliminate these taxes. Table 7.1 gives the payoffs from each of the possible outcomes. A's payoff is listed first.

If we modeled this game in the normal form, we would ignore that B knows A's choice when B makes its decision.