Question

Consider again the game with two players deciding how much to donate for a party. However suppose now that Player 1 makes her donation first, and observing how much Player 1 has donated, Player 2 makes his donation. Let dy be the amount donated by player 1 and d2 the amount donated by player 2, where both d1 and d2 are nonnegative real numbers. Once the money is donated players cannot get it back, no matter whether the party is organized or not. They will be able to organize the party if and only if the sum of their donations is more than or equal to 120 dollars i.e., di + d2 120 If they organize the party, Player 1's payoff is T1 = 100-d1, Player 2's payoff is T2 = 40 - dz. If they do not organize the party, their payoffs are ny = - di and 12 = -d2 and the amount Player 2 donates is (Please, enter only integer values here, for In a SPNE Player 1's payoff is example: 0, 15, 30, 101, etc).

Answer 1

Please find highlighted below the correct answers to the question along with a brief explanation to the same:

In a SPNE Player 1’s payoff is 90 and the amount Player 2 donates is 30

                            Explanation: SPNE stands for Sub-game Nash Equilibrium, which focuses on the various sub-game equilibriums that exist in between when a game is played. In this case, the total amount of donation for the party to happen is at least $120, and the payoff amount for layer 1 is 100-d1 and for Player 2 is 20-d2. Therefore, the if we calculate their Nash equilibrium at mid-game or sub-game level, then their total investment being 120 at least, the division factor of both players 1 and 2 would be (100-90=10) and (40-30=10) which therefore satisfies the sub-game requirement. Hence the Player 1’s payoff will be 90 and the amount Player 2 donates will be 30