game theory

Suppose Microsoft and Celera are considering a joint venture to use con sumer's genetic ngerprints as license keys for software registration. How ever, 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. Suppose that there are two possible types of Microsoft: Friend and Enemy. Microsoft knows its own type, but Celera. knows only that two types are equally likely. (a) Consider the following dynamic game. Microsoft has some Celera stock, and it can either \"Buy\" more or \"Sell\" what it is holding. Celera observes Microsoft's action and then decides whether to \"Reveal\" or \"Hide\" its pr0prietary trade secrets. This game is shown in extensive form in the illustration that follows. Microsoft's payo' are listed rst. Represent this game in the normal form. 5, 6 SR 15, 12 BR C FS MF FB C 5, -1 4 SH BH F (1/2) -1, 1 ON 15, -14 E (1/2) 5, -6 SR BR ES EB ME SH BH 0. -1 5, 1 (b) Find Bayesian Nash equilibria in (a). (c) Does the game in (a) has any pooling or separating equilibria? if so, describe them