Game Theory

4. [24 points] Microsoft and Celera are considering a joint venture to use consumersl genetic ngerprints as license keys for software registration. However, in a joint venture there is always the possibility that one partner is trying to extract proprietary trade secrets from the other, rather than trying to earn a joint prot. In this case: Celera is worried that Microsoft may be an Enemy, which happens with probability 0.5, rather than a Friend, which happens with probability 0.5. This probability distribution is commonly known, but only Microsoft knows its own true type. Consider the following dynamic game. Microsoft has some Celera stock: and it can either Buy more, or Sell what it is holding. Celera then observes Microsoft's action. and then decides whet-her to Reveal or Hide its proprietary trade secrets. This game is shown in extensive form below; Microsoft's payoffs are listed rst. (5.6) (15.12} km- 1:5 MP EFF-"f. 2:. PB .: 5'\" E E 3*: (5.4) r" ; r s ; \"W. (1.1) f: N ('3 {15-441 k E \"1 __..a (Eh6] S); : I '9\" : ES EB .: 51:1 ME 3,! {0.4; 0/ \"H: (5.11 [a] [12 points] Does the game have a separating equilibrium? If yes, construct one. If not, explain why