Game Theory Economics If its stage game has exactly one Nash equilibrium, how many subgame perfect...
Homework Answers
Answer:
Repeated game is a special type of game where the same one shot stage game is played over and over again. If it's a finite repeated game, then the game is played a known no. Of times. A finitely repeated game can have more than one SPNE if the stage game has more than one Nash equilibrium, but if the stage game has only one Nash equilibrium i.e. unique Nash equilibrium, then the only SPNE is to repeat this equilibrium in each period.
So, in a finite repeated game(two period) with stage game has unique Nash equilibrium, can have one SPNE. The result will be the same as long as T is finite integer.
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Game Theory Economics
If its stage game has exactly one Nash equilibrium, how many
subgame perfect...
4. If its stage game has exactly one Nash equilibrium, how many subgame perfect equilibria does...
4. If its stage game has exactly one Nash equilibrium, how many subgame perfect equilibria does a two-period, repeated game have? Explain. Would your answer change if there were Tperiods, where Tis any finite integer?
GAME THEORY: Suppose a stage game has exactly one nash equilibrium Suppose a stage game has...
GAME THEORY: Suppose a stage game has exactly one nash
equilibrium
Suppose a stage game has exactly one Nash equilibrium (select all that apply) a. In a finitely repeated game where players become more patient results other than the stage NE become feasible. b In the SPNE of the twice repeated game players play the stage NE in both periods. C.The Folk Theorem introduced in the notes assumes that actions are observable. d. In a finitely repeated game where T...
QUESTION Suppose a stage game has exactly one Nash equilibrium (select all that apply) a Any...
QUESTION Suppose a stage game has exactly one Nash equilibrium (select all that apply) a Any outcome can be supported as a SPNE when the game is repeated infinitely many times and players are patient enough. b. In a finitely repeated game where T becomes large, different outcomes can be supported as SPNE C. The Folk Theorem introduced in the notes assumes that actions are observable. d. In the SPNE of the twice repeated game players play the stage NE...
Game theory question (undergraduate economics) Consider the infinitely repeated game with the following stage game matrix:...
Game theory question (undergraduate economics)
Consider the infinitely repeated game with the following stage game matrix: C D C 3,2 0,1 D 7,0 2,1 Under what conditions is there a subgame perfect equilibrium in which the players alternate between (C,C) and (C,D), starting with (C,C) in the first period? Under what conditions is there a subgame perfect equilibrium in which the players alternate between (C,C) and (D,D), starting with (C,C) in the first period? (Use modified trigger strategies)
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...
. Player 1 and Player 2 are going to play the following stage game twice:
. 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...
1. Consider the following normal form game: 112 L CR T 10 102 12 0 13...
1. Consider the following normal form game: 112 L CR T 10 102 12 0 13 M 12 25 5 0 0 B|13 010 011 a) (Level A) First suppose this game is played only once. What are the pure strategy Nash equilibria? (b) (Level B) Now suppose this game is played twice. Players observe the actions chosen in the first period prior to the second period. Each player's total payoff is the sum of his/her payoff in the two...
1. Consider the following normal form game 112 L CR T|10 1012 1210 13 M 12...
1. Consider the following normal form game 112 L CR T|10 1012 1210 13 M 12 25 5 0 (0 B113 0100 (a) (Level A) First suppose this game is played only once. What are the pure strategy Nash equilibria? (b) (Level B) Now suppose this game is played twice. Players observe the actions chosen in the first period prior to the second period. Each player's total payoff is the sum of his/her payoff in the two periods. Consider the...
6. The following stage game is played repeatedly for 2 periods. Note that both players observe...
6. The following stage game is played repeatedly for 2 periods. Note that both players observe the decisions made in period 1 before they play again in period 2. The final payoffs to each player are the sum of the payoffs obtained in each period. 112 L R T 1,1 5,0 B 0,3 7,7 (a) Represent this game in extensive form (tree diagram. How many subgames are there? (b) Using backward induction, find all subgame perfect Nash equilibria (SPE) in...
Consider the infinitely repeated version of the symmetric two-player stage game in figure PR 13.2. The first number in a cell is player 1's single-period payoff. Assume that past actions are commo...
Consider the infinitely repeated version of the symmetric
two-player stage game in figure PR 13.2. The first number in a cell
is player 1's single-period payoff. Assume that past actions are
common knowledge. Each player's payoff is the present value of the
stream of single-period payoffs where the discount factor is d. (a)
Derive the conditions whereby the following strategy profile is a
subgame perfect Nash Equilibrium:
2 Consider the infinitely repeated version of the symmetric two-player stage game in...
4. If its stage game has exactly one Nash equilibrium, how many subgame perfect equilibria does a two-period, repeated game have? Explain. Would your answer change if there were Tperiods, where Tis any finite integer?
GAME THEORY: Suppose a stage game has exactly one nash
equilibrium
Suppose a stage game has exactly one Nash equilibrium (select all that apply) a. In a finitely repeated game where players become more patient results other than the stage NE become feasible. b In the SPNE of the twice repeated game players play the stage NE in both periods. C.The Folk Theorem introduced in the notes assumes that actions are observable. d. In a finitely repeated game where T...
QUESTION Suppose a stage game has exactly one Nash equilibrium (select all that apply) a Any outcome can be supported as a SPNE when the game is repeated infinitely many times and players are patient enough. b. In a finitely repeated game where T becomes large, different outcomes can be supported as SPNE C. The Folk Theorem introduced in the notes assumes that actions are observable. d. In the SPNE of the twice repeated game players play the stage NE...
Game theory question (undergraduate economics)
Consider the infinitely repeated game with the following stage game matrix: C D C 3,2 0,1 D 7,0 2,1 Under what conditions is there a subgame perfect equilibrium in which the players alternate between (C,C) and (C,D), starting with (C,C) in the first period? Under what conditions is there a subgame perfect equilibrium in which the players alternate between (C,C) and (D,D), starting with (C,C) in the first period? (Use modified trigger strategies)
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...
1. Consider the following normal form game: 112 L CR T 10 102 12 0 13 M 12 25 5 0 0 B|13 010 011 a) (Level A) First suppose this game is played only once. What are the pure strategy Nash equilibria? (b) (Level B) Now suppose this game is played twice. Players observe the actions chosen in the first period prior to the second period. Each player's total payoff is the sum of his/her payoff in the two...
1. Consider the following normal form game 112 L CR T|10 1012 1210 13 M 12 25 5 0 (0 B113 0100 (a) (Level A) First suppose this game is played only once. What are the pure strategy Nash equilibria? (b) (Level B) Now suppose this game is played twice. Players observe the actions chosen in the first period prior to the second period. Each player's total payoff is the sum of his/her payoff in the two periods. Consider the...
6. The following stage game is played repeatedly for 2 periods. Note that both players observe the decisions made in period 1 before they play again in period 2. The final payoffs to each player are the sum of the payoffs obtained in each period. 112 L R T 1,1 5,0 B 0,3 7,7 (a) Represent this game in extensive form (tree diagram. How many subgames are there? (b) Using backward induction, find all subgame perfect Nash equilibria (SPE) in...
Consider the infinitely repeated version of the symmetric
two-player stage game in figure PR 13.2. The first number in a cell
is player 1's single-period payoff. Assume that past actions are
common knowledge. Each player's payoff is the present value of the
stream of single-period payoffs where the discount factor is d. (a)
Derive the conditions whereby the following strategy profile is a
subgame perfect Nash Equilibrium:
2 Consider the infinitely repeated version of the symmetric two-player stage game in...
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