Game Theory

1. [24 points] Microsoft and Celera are considering a joint venture to use consumers' genetic fingerprints 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 profit. 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 whether to Reveal or Hide its proprietary trade secrets. This game is shown in extensive form below; Microsoft's payoffs are listed first. (5,6)SR (15,12) MF BR FS - FB - SH (5,-1) BH (-1,1) ON E 14 (15,-14)SR (5,-6) BK ES . EB SH ME BH - (0,-1) (5,1) (b) [6 points] Does the game have a pooling equilibrium in which both types of Microsoft play "Sell", (i.e., the strategy (FS, ES))? If yes, construct one. If not, explain why. (c) [6 points] Does the game have a pooling equilibrium in which both types of Microsoft play "Buy", (i.e., the strategy (FB, EB))? If yes, construct one. If not, explain why