Question: Aggie and Baggie are each armed with a single coconut cream pie. Since they are the friends of Larry and Curly, naturally, instead of eating the pies they are going to throw them at each other. Aggie goes first. At 20 paces she has the option of hurling the pie at Baggie or passing. Baggie then has the same choices at 20 paces but if Aggie hurls her pie and misses, the game is over because Aggie has no more pies. The game could go into a second round but now at 10 paces, and then a third round at 0 paces. Aggie and Baggie have the same probability of hitting the target at each stage: 1 3 at 20 paces, 3 4 at 10 paces, and 1 at 0 paces. If Baggie gets a pie in the face, Aggie scores +1, and if Aggie gets a pie in the face Baggie scores +1. This is a zero sum game.
(a) Draw the game tree and convert to a matrix form game.
(b) Solve the game.