Please Explain in steps thanks! Two partners would like to complete a project. E
ID: 1193292 • Letter: P
Question
Please Explain in steps thanks!
Two partners would like to complete a project. Each partner receives the payoff V when the project is completed but neither receives any payoff before completion. The cost remaining before the project can be complete is R. Neither partner can commit to making a future contribution towards completing the project, so they decide to play the following two-period game:
(f) In period 1,given player2’s response,will player1’s optimal investment level be c1=R? If so, state the condition under which this is the case. (This is challenging, but try your best.)
(i) If player1 does not invest in period1,will player2 invest in period2? In other words, is it possible that player 2 will fund this project alone? Brie?y explain. (hint: use results from part (a) and part (h); you can use math to show this result)
(j) Describe the subgame-perfect Nash Equilibrium(a) of this game.
(k) Interpret how the equilibrium behaves responding to changes by ?lling “increases”, “decrease” or “unclear” in the following table.
Explanation / Answer
When c1 = R,
then player 1’s payoff = V – R2
Player 2’s payoff = V
When c1 < R, then
(i) If player 2 puts in c2 = R – c1, then
player 1’s payoff = V – c12
Player 2’s payoff = V – (R– c1)2
(ii) If player 2 puts in c2 = 0, then
player 1’s payoff = – c12
Player 2’s payoff = 0
The game tree is the following
Player 2 will put in c2 = R – c1 if
c1 < R
and V – (R– c1)2 0
V (R – c1)2
c1 R – V
that is, Player 2 will put in c2 = R – c1 if
R – V c1 < R
Player 2 will put in c2 = 0, when
c1 < R – V
So the game is the following
In the range R – V c1 < R, player 1 will always choose c1 = R – V. Therefore the game is: