Consider a game with two players deciding simultaneously how much to donate for a party. Let...
Consider a game with two players deciding simultaneously how
much to donate for a party. Let d1 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 150 dollars i.e.,
If they organize the party, Player 1's payoff is
, Player 2's payoff is
. If they do not organize the party, their payoffs are
and
.
Which of the following are Nash equilibrium donations (select all that apply)
| a. |
d1 =0 and d2 =0. |
|
| b. |
d1 =90 and d2 =90. |
|
| c. |
d1 =90 and d2 =60. |
|
| d. |
d1 =75 and d2 =75. |
Homework Answers
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Consider a game with two players deciding simultaneously how much to donate for a party. Let...
Please help!!! Game theory Consider a game with two players deciding simultaneously how much to donate...
Please help!!! Game theory Consider a game with two players deciding simultaneously how much to donate for a party. Let d1 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...
Consider a game with two players deciding simultaneously how much to donate tor a party. Let...
Consider a game with two players deciding simultaneously how much to donate tor a party. Let d be the amcunt donated by player 1 and dy the amount donated by player 2, where both di and d are nonnegative real numbers. Once the money is donated players. cannot get i 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 donaticns is mcre than...
Consider again the game with two players deciding how much to donate for a party. However...
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...
First part: Consider the following two-player game. The players simultaneously and independently announce an integer number...
First part: Consider the following two-player game. The players simultaneously and independently announce an integer number between 1 and 100, and each player's payoff is the product of the two numbers announced. (a) Describe the best responses of this game. How many Nash equilibria does the game have? Explain. (b) Now, consider the following variation of the game: first, Player 1 can choose either to "Stop" or "Con- tinue". If she chooses "Stop", then the game ends with the pair...
4. Consider the following game that is played T times. First, players move simultaneously and independently....
4. Consider the following game that is played T times. First, players move simultaneously and independently. Then each player is informed about the actions taken by the other player in the first play and, given this, they play it again, and so on. The payoff for the whole game is the sum of the payoffs a player obtains in the T plays of the game A 3,1 4,0 0,1 В 1,5 2,2 0,1 C 1,1 0,2 1,2 (a) (10%) Suppose...
Consider the following version of the Rock-Paper-Scissors game. The two players have to choose simultaneously between...
Consider the following version of the Rock-Paper-Scissors game.
The two players have to choose simultaneously between
Rock(R), Paper(P) or Scissors(S).
According to this game, R beats S, S
beats P, P beats R. The winner gets 1
dollar from the other player. In case of a tie,the referee gives
both players 2 dollars. Payoffs for all possible choices are
summarized in the table below. Find all Nash Equilibria.
3) (25 points) Consider the following version of the Rock-Paper-Scissors game. The...
1. Consider the coupon game. But suppose that instead of decisions being made simultaneously, they are made sequentially, with Firm 1 choosing first, and its choice observed by Firm 2 before Firm 2 ma...
1. Consider the coupon game. But suppose that instead of
decisions being made simultaneously, they are made sequentially,
with Firm 1 choosing first, and its choice observed by Firm 2
before Firm 2 makes its choice.
a. Draw a game tree representing this game.
b. Use backward induction to find the solution. (Remember that
your solution should include both firms’ strategies, and that Firm
2’s strategy should be complete!)
2. Two duopolists produce a homogeneous product, and each has a...
Consider a game with two players deciding simultaneously how much to donate tor a party. Let d be the amcunt donated by player 1 and dy the amount donated by player 2, where both di and d are nonnegative real numbers. Once the money is donated players. cannot get i 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 donaticns is mcre than...
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...
First part: Consider the following two-player game. The players simultaneously and independently announce an integer number between 1 and 100, and each player's payoff is the product of the two numbers announced. (a) Describe the best responses of this game. How many Nash equilibria does the game have? Explain. (b) Now, consider the following variation of the game: first, Player 1 can choose either to "Stop" or "Con- tinue". If she chooses "Stop", then the game ends with the pair...
4. Consider the following game that is played T times. First, players move simultaneously and independently. Then each player is informed about the actions taken by the other player in the first play and, given this, they play it again, and so on. The payoff for the whole game is the sum of the payoffs a player obtains in the T plays of the game A 3,1 4,0 0,1 В 1,5 2,2 0,1 C 1,1 0,2 1,2 (a) (10%) Suppose...
Consider the following version of the Rock-Paper-Scissors game.
The two players have to choose simultaneously between
Rock(R), Paper(P) or Scissors(S).
According to this game, R beats S, S
beats P, P beats R. The winner gets 1
dollar from the other player. In case of a tie,the referee gives
both players 2 dollars. Payoffs for all possible choices are
summarized in the table below. Find all Nash Equilibria.
3) (25 points) Consider the following version of the Rock-Paper-Scissors game. The...
1. Consider the coupon game. But suppose that instead of
decisions being made simultaneously, they are made sequentially,
with Firm 1 choosing first, and its choice observed by Firm 2
before Firm 2 makes its choice.
a. Draw a game tree representing this game.
b. Use backward induction to find the solution. (Remember that
your solution should include both firms’ strategies, and that Firm
2’s strategy should be complete!)
2. Two duopolists produce a homogeneous product, and each has a...
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