Player 1 can choose to either play against Player 2 or Player 3. If she chooses...
Player 1 can choose to either play against Player 2 or Player 3. If she chooses to play against Player 2, Player 2 gets to choose between moves X and and Y, and Player 1 picks between moves C and D. If Player 1 chooses to play against Player 3, Player 3 gets a choice between moves S and T, and Player 1 gets to choose between moves E and F.
The payoffs for each combination of moves are as follows:
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P1 Plays Against P2 |
P1 Plays Against P3 |
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- Put the game into a tree in which the players all have perfect information.
- Alter the tree so that now after Player 1 makes the choice on who to play against (which all players observe), she and her opponent make their moves simultaneously.
Homework Answers
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Player 1 can choose to either play against Player 2 or Player 3.
If she chooses...
2. Consider the following sequential game. Player A can choose between two tasks, Tl and T2....
2. Consider the following sequential game. Player A can choose between two tasks, Tl and T2. After having observed the choice of A, Player B chooses between two projects Pl or P2. The payoffs are as follows: If A chooses TI and B chooses P1 the payoffs are (12, 8), where the first payoff is for A and the second for B; if A chooses T1 and B opts for P2 the payoffs are (20, 7); if A chooses T2...
2. Consider the following sequential game. Player A can choose between two tasks, TI and T2....
2. Consider the following sequential game. Player A can choose between two tasks, TI and T2. After having observed the choice of A, Player B chooses between two projects P1 or P2. The payoffs are as follows: If A chooses TI and B chooses Pl the payoffs are (12.8), where the first payoff is for A and the second for B; if A chooses TI and B opts for P2 the payoffs are (20,7); if A chooses T2 and B...
6. Consider a sequential game with 3 players. Player 1 can choose A or B. Player...
6. Consider a sequential game with 3 players. Player 1 can choose A or B. Player 2 can choose C, D, E, or F (depending on what player 1 chooses). Player 3 can choose G, H, I, J, K, L, M, or N (depending on what player 1 and 2 choose). Player 1 (P1) goes first, player 2 (P2) goes second, and player 3 (P3) goes third. Payoffs are written as the payoffs for P1, P2, and the for P3....
Elina has to choose between two projects, P1 and P2. If Elina chooses P1 the game is over and the payoffs are 4 to...
Elina has to choose between two projects, P1 and P2. If Elina chooses P1 the game is over and the payoffs are 4 to Elina and 13 to Bonnie. If Elina choose P2, Bonnie observes Elina's choice and then gets to choose between projects P3 and P4. If Elina chooses P2 and Bonnie chooses P3 the payoffs are 2 to Elina and 8 to Bonnie. If Elina chooses P2 and Bonnie chooses P4 the payoffs are 5 and 10 to...
3. (15 points) Consider a sequential game with two players with three-moves, in which player 1...
3. (15 points) Consider a sequential game with two players with three-moves, in which player 1 moves twice: Player 1 chooses Enter or Erit, and if she chooses Exit the game ends with payoffs of 2 to player 2 and 0 to player 1. • Player 2 observes player l's choice and will have a choice between Fight or Help if player 1 chose Enter. Choosing Help ends the game with payoffs of 1 to both players. • Finally, player...
Consider a game being played between player 1 and player 2. Player 1 can choose T...
Consider a game being played between player 1 and player 2. Player 1 can choose T or B. Player 2 can take actions Lor R. These choices are made simultaneously. The payoffs are as follows. If 1 plays T and 2 plays L, the payoffs are (0,0) for Player 1 and 2, respectively. If 1 opts of B and 2 L, the payoffs are (5,7). If 1 plays T and 2 R, the payoffs are (6,2). Finally, both players get...
Consider a game being played between player 1 and player 2. Player 1 can choose T...
Consider a game being played between player 1 and player 2. Player 1 can choose T or B. Player 2 can take actions Lor R. These choices are made simultaneously. The payoffs are as follows. If 1 plays T and 2 plays L, the payoffs are (0, 0) for Player 1 and 2, respectively. If 1 opts of B and 2 L, the payoffs are (5,7). If 1 plays T and 2 R, the payoffs are (6,2). Finally, both players...
3 3 Player Games Suppose there are 3 players, PI, P2 and P3, with feasible strategies...
3 3 Player Games Suppose there are 3 players, PI, P2 and P3, with feasible strategies S = {U,D), S2 L, R, S3 - {A, B). The payoffs are summarized in the following payoff matrices: Table 3: Payoff Matrices P3 P3 plays A P2 P3 plays B P2 U|3,3,8 1,2,-2 D 0,9,6 -4,13 , -2 ,1 U 11,-1,2 9,5,12 DI 0,1,4 3,-1 , 3 P1 where in an cell the payoff x , y , z corresponds to P1, P2...
Game: Extensive Form. Suppose player 1 chooses G or H, and player 2 observes this choice....
Game: Extensive Form. Suppose player 1 chooses G or H, and player 2 observes this choice. If player 1 chooses H, then player 2 must choose A or B. Player 1 does not get to observe this choice by player 2, and must then choose X or Y. If A and X are played, the payoff for player 1 is 1 and for player 2 it's 5. If A and Y are played, the payoff for player 1 is 6...
3. Player 1 and Player 2 are going to play the following stage game twice: &n...
3. Player 1 and Player 2 are going to play the following stage
game twice:
Player 2
Left
Middle
Right
Player 1
Top
4, 3
0, 0
1, 4
Bottom
0, 0
2, 1
0, 0
There is no discounting in this problem and so a player’s payoff
in this repeated game is the sum of her payoffs in the two plays of
the stage game.
(a) Find the Nash equilibria of the stage game. Is (Top, Left) a...
2. Consider the following sequential game. Player A can choose between two tasks, Tl and T2. After having observed the choice of A, Player B chooses between two projects Pl or P2. The payoffs are as follows: If A chooses TI and B chooses P1 the payoffs are (12, 8), where the first payoff is for A and the second for B; if A chooses T1 and B opts for P2 the payoffs are (20, 7); if A chooses T2...
2. Consider the following sequential game. Player A can choose between two tasks, TI and T2. After having observed the choice of A, Player B chooses between two projects P1 or P2. The payoffs are as follows: If A chooses TI and B chooses Pl the payoffs are (12.8), where the first payoff is for A and the second for B; if A chooses TI and B opts for P2 the payoffs are (20,7); if A chooses T2 and B...
Elina has to choose between two projects, P1 and P2. If Elina chooses P1 the game is over and the payoffs are 4 to Elina and 13 to Bonnie. If Elina choose P2, Bonnie observes Elina's choice and then gets to choose between projects P3 and P4. If Elina chooses P2 and Bonnie chooses P3 the payoffs are 2 to Elina and 8 to Bonnie. If Elina chooses P2 and Bonnie chooses P4 the payoffs are 5 and 10 to...
3. (15 points) Consider a sequential game with two players with three-moves, in which player 1 moves twice: Player 1 chooses Enter or Erit, and if she chooses Exit the game ends with payoffs of 2 to player 2 and 0 to player 1. • Player 2 observes player l's choice and will have a choice between Fight or Help if player 1 chose Enter. Choosing Help ends the game with payoffs of 1 to both players. • Finally, player...
Consider a game being played between player 1 and player 2. Player 1 can choose T or B. Player 2 can take actions Lor R. These choices are made simultaneously. The payoffs are as follows. If 1 plays T and 2 plays L, the payoffs are (0,0) for Player 1 and 2, respectively. If 1 opts of B and 2 L, the payoffs are (5,7). If 1 plays T and 2 R, the payoffs are (6,2). Finally, both players get...
Consider a game being played between player 1 and player 2. Player 1 can choose T or B. Player 2 can take actions Lor R. These choices are made simultaneously. The payoffs are as follows. If 1 plays T and 2 plays L, the payoffs are (0, 0) for Player 1 and 2, respectively. If 1 opts of B and 2 L, the payoffs are (5,7). If 1 plays T and 2 R, the payoffs are (6,2). Finally, both players...
3 3 Player Games Suppose there are 3 players, PI, P2 and P3, with feasible strategies S = {U,D), S2 L, R, S3 - {A, B). The payoffs are summarized in the following payoff matrices: Table 3: Payoff Matrices P3 P3 plays A P2 P3 plays B P2 U|3,3,8 1,2,-2 D 0,9,6 -4,13 , -2 ,1 U 11,-1,2 9,5,12 DI 0,1,4 3,-1 , 3 P1 where in an cell the payoff x , y , z corresponds to P1, P2...
3. Player 1 and Player 2 are going to play the following stage
game twice:
Player 2
Left
Middle
Right
Player 1
Top
4, 3
0, 0
1, 4
Bottom
0, 0
2, 1
0, 0
There is no discounting in this problem and so a player’s payoff
in this repeated game is the sum of her payoffs in the two plays of
the stage game.
(a) Find the Nash equilibria of the stage game. Is (Top, Left) a...
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