game theory

Consider the following two-player team production game. The players simultaneously chooses effort levels (al for player 1 and :12 for player 2), and revenue is given by 2k(a1 + (12). Suppose that player i's cost of effort is 0.12- in monetary terms. Revenue is split equally between the players, so, player i's payoff is Mal + a2) (1?. Assume that the value of k is privately observed by player 1 prior to her selection of a1. Player 2 does not know the value of k before choosing (32. Player 2 knows only that k is either 4 or 8, with these being equally likely. (a) Find the Bayesian Nash Equilibrium (effort levels) for this game. (b) Consider a variation of the game in which, after observing k and the prior to effort selection, player 1 can provide evidence of the value of k to player 2. That is, after either realization of 14:, player 1 chooses either E or N. If she selects E, then )6 is revealed to player 2; otherwise, player 2 observes nothing other than that player 1 selected N. Represent this game in extensive form and calculate the perfect Bayesian equilibria. Are there any perfect Bayesian equilibria. in which, at the time player 2 selects (12, she is uncertain of k? (c) Would player 1 prefer to have the Option of revealing k, as in part (b) relative to part (a)? Explain