Which strategy or strategies are strictly dominated, and which one is weakly dominated?
A.Gun & Show
B.Gun & Hide
C.No Gun
D.RR
E.RN
F.NR
G.NN
H.None of the strategies are strictly dominated
Homework Answers
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Which strategy or strategies are strictly dominated, and which
one is weakly dominated?
A.Gun & Show...
Which strategy or strategies are strictly dominated, and which one is weakly dominated? A. Gun &...
Which strategy or strategies are strictly dominated, and which
one is weakly dominated?
A.
Gun & Show
B.
Gun & Hide
C.
No Gun
D.
RR
E.
RN
F.
NR
G.
NN
H.
None of the strategies are strictly dominated
Mugger Gun & show No gun Gun & hide Simon Simon Do not resist Do not resist Do not resist Resist Resist Resist Mugger 34 Simon 2 3 5 2 6 5 2 4 6 3
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
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...
Exercise 4 - Pure strategies that are only strictly dominated by a mixed strategy Consider the...
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...
2. Iterative Deletion of (weakly) Dominated Strategies Consider the following two-player game 2 I c I...
2. Iterative Deletion of (weakly) Dominated Strategies Consider the following two-player game 2 I c I T 1,1 0,1 3,1 1 M 1,0 2,2 1,3 D 1,3 3,1 2,2 (a) Are there any strictly dominated strategies? Are there any weakly dominated strategies? If so, explain what dominates what and how. (b) After deleting any strictly or weakly dominated strategies, are there any strictly or weakly dominated strategies in the reduced' game? If so, explain what dominates what and how. What...
survive 1.2. In the following normal-form game, what strategies survive iterated elimination of strictly dominated strategies?...
survive 1.2. In the following normal-form game, what strategies survive iterated elimination of strictly dominated strategies? What are the pure-strategy Nash equilibria? of strictly dominated L CR T 2,0 1,14,2 M 3,4 1,2 2,3 B 1,30,2 3,0
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...
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...
2. (5 marks total IEDS practice Use iterated elimination of dominated strategies to reduce the following...
2. (5 marks total IEDS practice Use iterated elimination of dominated strategies to reduce the following games. We will call the row player P1 and the column player P2; note that for each entry in the payoff matrices below, PI's payoff is listed first. Clearly indicate: the order in which you eliminate strategies; whether the eliminated strategy is strictly or weakly dominated; If you find a dominant strategy equilibrium, state what it is. Is it unique? 81 (1,5) 50, -11)...
) 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
Which strategy or strategies are strictly dominated, and which
one is weakly dominated?
A.
Gun & Show
B.
Gun & Hide
C.
No Gun
D.
RR
E.
RN
F.
NR
G.
NN
H.
None of the strategies are strictly dominated
Mugger Gun & show No gun Gun & hide Simon Simon Do not resist Do not resist Do not resist Resist Resist Resist Mugger 34 Simon 2 3 5 2 6 5 2 4 6 3
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
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...
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...
2. Iterative Deletion of (weakly) Dominated Strategies Consider the following two-player game 2 I c I T 1,1 0,1 3,1 1 M 1,0 2,2 1,3 D 1,3 3,1 2,2 (a) Are there any strictly dominated strategies? Are there any weakly dominated strategies? If so, explain what dominates what and how. (b) After deleting any strictly or weakly dominated strategies, are there any strictly or weakly dominated strategies in the reduced' game? If so, explain what dominates what and how. What...
survive 1.2. In the following normal-form game, what strategies survive iterated elimination of strictly dominated strategies? What are the pure-strategy Nash equilibria? of strictly dominated L CR T 2,0 1,14,2 M 3,4 1,2 2,3 B 1,30,2 3,0
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...
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...
2. (5 marks total IEDS practice Use iterated elimination of dominated strategies to reduce the following games. We will call the row player P1 and the column player P2; note that for each entry in the payoff matrices below, PI's payoff is listed first. Clearly indicate: the order in which you eliminate strategies; whether the eliminated strategy is strictly or weakly dominated; If you find a dominant strategy equilibrium, state what it is. Is it unique? 81 (1,5) 50, -11)...
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