Student Activity Play VNM-Poker in the applet VNMPokerseq13. The description can be found there.

Student Activity Play 2-round WAITING FOR MR. PERFECT in the applet Waiting2b.

Chapter 2 was about simultaneous games. We showed how a matrix representation, the normal form, can be helpful in analyzing a game. In Chapters 8 and 16, which dealt with sequential games with or without randomness, we learned how to describe such games in extensive form, and how these games have a clearly defined solution and (expected) value, which we can compute using backward induction. An important assumption was that we had perfect information about the games.

However, most games are neither simultaneous nor purely perfect-information sequential. They are something in between. Some are essentially sequential with some moves done in parallel, like WAITING FOR MR PERFECT; some are sequential but lack perfect information like VNM-POKER. Perfect information means that every player is aware of all previous moves of all players. Simultaneous moves can be rephrased as sequential moves with non-perfect information–we put them into any order without giving the player who moves second knowledge about the move of the player moving first. In this chapter we will see that the description in extensive form can be applied to any game, even one with imperfect information.