Consider the following two-player team production problem. The players simultaneously choose effort levels (a1 for player 1 and a2 for player 2), and revenue is given by 2k[a₁ + a₂]. Suppose that player i's cost of effort is a2 i in monetary terms. Revenue is split equally between the players, so player i's payoff is k[a₁ + a₂] - a₂  . 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 a2 . 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 prior to effort selection, player 1 can provide evidence of the value of k to player 2. That is, after either realization of k, player 1 chooses either E or N. If she selects E, then k is revealed to player 2; otherwise, player 2 observes nothing other than that player 1 selected N. Represent this game in the extensive form and calculate the perfect Bayesian equilibria. Are there any perfect Bayesian equilibria in which, at the time player 2 selects a₂ , 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.