![Exercise 4 - Pure strategies that are only strictly dominated by a mixed strategy Consider the following normal form game Player 2 Left Right Player 1 4,1 Down 13 12 b) Is there some strictly dominated strategy for player 1 when mixed strategies are allowed? [Hint: 0,2 4,1 Middle0,0 a) c) d) Is there some strictly dominated strategy for player 1 involving only the use of pure strategies? you may assign probabilities to two of her strategies, similarly as we did in class]. Delete the strictly dominated strategies for player 2 that you found in the previous question. Then, represent the remaining (undeleted) strategies. Proceed with IDSDS. What is the strategy pair surviving IDSDS?](http://img.homeworklib.com/questions/3a6ee040-4c8d-11ea-a0e2-8debfb3c21d7.png?x-oss-process=image/resize,w_560)
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Exercise 4 - Pure strategies that are only strictly dominated by a mixed strategy Consider the...
1. (Dominated Strategies) Find strictly dominant strategy, strictly dominated strategy, weakly dominant strategy, and weakly dominated...
1. (Dominated Strategies) Find strictly dominant strategy, strictly dominated strategy, weakly dominant strategy, and weakly dominated strategy of the following two games("None" may be an answer). Do not forget to discuss about mixed strategies too. (a) (Keio and Waseda) Player 2 K E O Wa 6,1 2,3 0,2 Player 1 Se 3,00,0,0 Da 2,0 1,2 01 b) (NHK BS) Player 2 BS N 41 0,2 Player 1 H 0,0 4,0 Problems 6 and 7 are in the next pages
IDSDS= Iterative Deletion of Strictly Dominated Strategies Exercise 3- Unemployment benefits. Consider the following simultaneous-move game...
IDSDS= Iterative Deletion of Strictly Dominated Strategies
Exercise 3- Unemployment benefits. Consider the following simultaneous-move game between the government (row player), which decides whether to offer unemployment benefits, and an unemployed worker (column player), who chooses whether to search for a job. As you interpret from the payoff matrix below, the unemployed worker only finds it optimal to search for a job when he receives no unemployment benefit; while the government only finds it optimal to help the worker when...
Iterated Iterated elimination of dominated strategies: Eliminate all strictly (weakly) dominated strategies for all players in...
Iterated
Iterated elimination of dominated strategies:
Eliminate all strictly (weakly) dominated strategies for all
players in the original game.
Eliminate all strictly (weakly) dominated strategies for all
players in the modified game where players cannot choose any
strategy that was eliminated at Step 1.
3 Eliminate all strictly (weakly) dominated strategies for all
players in the modified game where players cannot choose any
strategy that was eliminated at Steps 1 and 2.
4 ...
and so on until there are...
Problem #3: Strictly dominated and non-rationalizable strategies (6 pts) Below, there are three game tables. For...
Problem #3: Strictly dominated and non-rationalizable strategies (6 pts) Below, there are three game tables. For each one, identify which strategies are non-rationalizable (if any), and which strategies are strictly dominated (if any). Do this for both players in each game. Note: You don't need to use IESDS or IENBR in this problem: I only want to know which strategies are strictly dominated or non-rationalizable in the games as presented. Rogers Go Rogue Go Legit 2,3 3,4 3,2 5,1 3,1...
Game Theory Nash Equilibrium Mixed strategies for 2*3 Matrix
a) Eliminate strictly dominated strategies.b) If the game does not have a pure strategy Nash equilibrium,find the mixed strategy Nash equilibrium for the smaller game(after eliminating dominated strategies). Player 2Player 1abcA4,33,22,4B1,35,33,3
(20 points) Exercise 3: (Midterm 2018) Consider the following normal-form game, where the pure strategies for...
(20 points) Exercise 3: (Midterm 2018) Consider the following normal-form game, where the pure strategies for Player 1 are U, M, and D, and the pure strategies for Player 2 are L, C, and R. The first payoff in each cell of the matrix belongs to Player 1, and the second one belongs to Player 2. Player 2 IL CR u 6,8 2,6 8,2 Player 1 M 8,2 4,4 9,5 8,10 4,6 6,7 (7) a) Find the strictly dominated (pure)...
4. Consider the following game matrix: LCR T 3 ,1 0,0 4,1 M10, 02, 24, 3...
4. Consider the following game matrix: LCR T 3 ,1 0,0 4,1 M10, 02, 24, 3 B 7,6 | 1,2 3,1 (a) Find all the strictly dominated (pure) strategies for each player. (b) Find all the weakly dominated (pure) strategies of each player. (c) Does the game has a strict dominant strategy equilibrium?
) Solve the game below by iterated elimination of strongly dominated strategies (Hint: One of the...
) Solve the game below by iterated elimination of strongly dominated strategies (Hint: One of the pure strategies for player 1 is strongly dominated by a mixed strategy). At each step of the elimination, state which pure strategy you are eliminating and which strategy (there can be more than one; just state one) it is strongly dominated by. X Y Z A 5,-2 0,1 6,0 B 2,8 2,3 1,4 C 0,0 7,1 -2,0
4. [20] Answer the following. (a) (5) State the relationship between strictly dominant strategies solution and...
4. [20] Answer the following. (a) (5) State the relationship between strictly dominant strategies solution and iterated elimination of strictly dominated strategies solution. That is, does one solution concept imply the other? (b) (5) Consider the following game: player 2 E F G H A-10,6 10.0 3,8 4.-5 player 1 B 9,8 14,8 4.10 2,5 C-10,3 5,9 8.10 5,7 D 0,0 3,10 8,12 0,8 Does any player have a strictly dominant strategies? Find the strictly dominant strategies solution and the...
Exercise 2 - A variation ofthe Prisoner's Dilemma game. Consider the following Prisoner's Dilemma game. The...
Exercise 2 - A variation ofthe Prisoner's Dilemma game. Consider the following Prisoner's Dilemma game. The game coincides with that we discussed in class, except for the fact that every player sees his payoff decrease by m>0 when he chooses to confess. For instance, prisoner 1's payoff decreases by m in the top row (where he confesses) but is unaffected when he is at the bottom row (where he does not confess). A similar argument applies to prisoner 2, who...
1. (Dominated Strategies) Find strictly dominant strategy, strictly dominated strategy, weakly dominant strategy, and weakly dominated strategy of the following two games("None" may be an answer). Do not forget to discuss about mixed strategies too. (a) (Keio and Waseda) Player 2 K E O Wa 6,1 2,3 0,2 Player 1 Se 3,00,0,0 Da 2,0 1,2 01 b) (NHK BS) Player 2 BS N 41 0,2 Player 1 H 0,0 4,0 Problems 6 and 7 are in the next pages
IDSDS= Iterative Deletion of Strictly Dominated Strategies
Exercise 3- Unemployment benefits. Consider the following simultaneous-move game between the government (row player), which decides whether to offer unemployment benefits, and an unemployed worker (column player), who chooses whether to search for a job. As you interpret from the payoff matrix below, the unemployed worker only finds it optimal to search for a job when he receives no unemployment benefit; while the government only finds it optimal to help the worker when...
Iterated
Iterated elimination of dominated strategies:
Eliminate all strictly (weakly) dominated strategies for all
players in the original game.
Eliminate all strictly (weakly) dominated strategies for all
players in the modified game where players cannot choose any
strategy that was eliminated at Step 1.
3 Eliminate all strictly (weakly) dominated strategies for all
players in the modified game where players cannot choose any
strategy that was eliminated at Steps 1 and 2.
4 ...
and so on until there are...
Problem #3: Strictly dominated and non-rationalizable strategies (6 pts) Below, there are three game tables. For each one, identify which strategies are non-rationalizable (if any), and which strategies are strictly dominated (if any). Do this for both players in each game. Note: You don't need to use IESDS or IENBR in this problem: I only want to know which strategies are strictly dominated or non-rationalizable in the games as presented. Rogers Go Rogue Go Legit 2,3 3,4 3,2 5,1 3,1...
(20 points) Exercise 3: (Midterm 2018) Consider the following normal-form game, where the pure strategies for Player 1 are U, M, and D, and the pure strategies for Player 2 are L, C, and R. The first payoff in each cell of the matrix belongs to Player 1, and the second one belongs to Player 2. Player 2 IL CR u 6,8 2,6 8,2 Player 1 M 8,2 4,4 9,5 8,10 4,6 6,7 (7) a) Find the strictly dominated (pure)...
4. Consider the following game matrix: LCR T 3 ,1 0,0 4,1 M10, 02, 24, 3 B 7,6 | 1,2 3,1 (a) Find all the strictly dominated (pure) strategies for each player. (b) Find all the weakly dominated (pure) strategies of each player. (c) Does the game has a strict dominant strategy equilibrium?
4. [20] Answer the following. (a) (5) State the relationship between strictly dominant strategies solution and iterated elimination of strictly dominated strategies solution. That is, does one solution concept imply the other? (b) (5) Consider the following game: player 2 E F G H A-10,6 10.0 3,8 4.-5 player 1 B 9,8 14,8 4.10 2,5 C-10,3 5,9 8.10 5,7 D 0,0 3,10 8,12 0,8 Does any player have a strictly dominant strategies? Find the strictly dominant strategies solution and the...
Exercise 2 - A variation ofthe Prisoner's Dilemma game. Consider the following Prisoner's Dilemma game. The game coincides with that we discussed in class, except for the fact that every player sees his payoff decrease by m>0 when he chooses to confess. For instance, prisoner 1's payoff decreases by m in the top row (where he confesses) but is unaffected when he is at the bottom row (where he does not confess). A similar argument applies to prisoner 2, who...
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