Suppose that two people (P1 and P2) are considering whether to form a partnership firm. P2's...

  

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Suppose that two people (P1 and P2) are considering whether to form a partnership firm. P2's productivity (type) is unknown to P1 at the time at which these people must decide whether to create a firm, but P1 knows that p = P[H] and 1-p=P[L] (for “high” and "low" types). P2 knows their own probability. If they don't form a firm, then their payoffs are zero. If they do form a firm, then their payoffs are as follows: if P2 is H, both get 10. If P2 is L P2 gets 5 and P1 gets -4 Consider the situation in which P1 can either form the firm F or not form the firm O. Draw the extensive form using a node for nature to draw the type of P2. What is the Bayesian Equilibrium of this game? (it depends on p) Now suppose that before P1 decides whether or not to form the firm P2 decides whether or not to give Pl a gift G or N, and P1 observes G or N before deciding on F or O. The gift costs P2 g units of utility. P1 gets w extra utility if they receive a gift. Draw the ex- tensive form of this game Under what conditions (on g and w) does a (separating) Perfect Bayesian Equilibrium exist in which the low type of P2 does not give a gift, while the high type does? Specify such an equilibrium (complete strategy profile and beliefs at each information set). Suppose that two people (P1 and P2) are considering whether to form a partnership firm. P2's productivity (type) is unknown to P1 at the time at which these people must decide whether to create a firm, but P1 knows that p = P[H] and 1-p=P[L] (for “high” and "low" types). P2 knows their own probability. If they don't form a firm, then their payoffs are zero. If they do form a firm, then their payoffs are as follows: if P2 is H, both get 10. If P2 is L P2 gets 5 and P1 gets -4 Consider the situation in which P1 can either form the firm F or not form the firm O. Draw the extensive form using a node for nature to draw the type of P2. What is the Bayesian Equilibrium of this game? (it depends on p) Now suppose that before P1 decides whether or not to form the firm P2 decides whether or not to give Pl a gift G or N, and P1 observes G or N before deciding on F or O. The gift costs P2 g units of utility. P1 gets w extra utility if they receive a gift. Draw the ex- tensive form of this game Under what conditions (on g and w) does a (separating) Perfect Bayesian Equilibrium exist in which the low type of P2 does not give a gift, while the high type does? Specify such an equilibrium (complete strategy profile and beliefs at each information set).