Consider a game with three players, Alan, Brad, and Cam. Alan moves rst and chooses ...

Consider a game with three players, Alan, Brad, and Cam. Alan moves rst and chooses either hot or warm or cold. Brad moves after Alan and observes what Alan has chosen. Brad chooses either Left or Right but his choice can depend on what Alan has done. Cam makes the next move, observing Brad's choice but not Alan's choice. So he knows that Brad has chosen Left or Right but not whether it followed hot, warm, or cold. Cam has two choices at each of his information sets, say H(igh) or L(ow). Finally, Alan moves again; he remembers, of course, what he has chosen but does not know what Brad or Cam has chosen. He has two choices in each of his information sets at this move, in or out.

a) Draw the extensive form of this game.

b) How many information sets does Alan have?

c) How many information sets does Brad have?

d) How many information sets does Cam have?

e) How many strategies does Alan have? What are they?

f) How many strategies does Brad have? What are they?

g) How many strategies does Cam have? What are they?