Iterated 
Iterated elimination of dominated strategies:
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Eliminate all strictly (weakly) dominated strategies for all players in the original game.
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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.
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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.
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4 ...
and so on until there are no new strictly (weakly) dominated strategies for any of the players.
Homework Answers
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Iterated
Iterated elimination of dominated strategies:
Eliminate all strictly (weakly) dominated strategies for all
players in...
Some notes: A hundred players are participating in this game (N 100). Each player has to...
Some notes:
A hundred players are participating in this game (N 100). Each player has to choose an integer between 1 and 100 in order to guess "5/6 of the average of the responses given by all players". Each player who guesses the integer closest to the 5/6 of the average of all the responses, wins (a) Q4 Find all weakly dominated strategies (if any). (b) Find all strategies that survive the Iterative Elimination of Dominated Strategies (IEDS) (if any)...
Q1 Elimination of strictly-dominated strategies In each of the following two-player games, what strategies survive iterated...
Q1 Elimination of strictly-dominated strategies In each of the following two-player games, what strategies survive iterated elimination of strictly- dominated strategies? Player 2 Lett Center Right Top 0.2 4, 3 3,1 Player1 Middle 1, 2 2,0 2, Bottom 2,4 36 0,3 Player 2 Left Center Right Top 1, 3 ,4 ,2 Player 1 Middle 2,2 2 3,1 Bottom 3, 5 43 1, 4
Q1 Elimination of strictly-dominated strategies In each of the following two-player games, what strategies survive iterated...
Q1 Elimination of strictly-dominated strategies In each of the following two-player games, what strategies survive iterated elimination of strictly- dominated strategies? What are the Nash equilibria of these games? (a) Player 2 Left 0,2 1,3 2,4 Top Middle Bottom Center 4,3 2,4 1,5 Right 3, 4 2, 3 4,6 Player 1 (b) Player 2 Left 2,4 3,3 4,6 Top Middle Bottom Center 6,5 4,3 5,4 Player 1 Right 5,3 4, 2 2,5
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)...
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
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
) 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
Game Theory Iterated Elimination: In the following normal-form game, which strategy profiles survive iterated elimination of...
Game Theory
Iterated Elimination: In the following normal-form game, which strategy profiles survive iterated elimination of strictly dominated strategies? 4.5 Player 2 L C R 6,8 2,6 8,2 Player 1 M 8,2 4,4 9,5 D 8,10 4,6 6,7
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...
(4) Using the Iterated elimination of (weakly) dominated strategy method, find all dom- inant strategy solutions...
(4) Using the Iterated elimination of (weakly) dominated strategy method, find all dom- inant strategy solutions of the following games P2 P2 L R Game 1: T 1,1 5,0 P M 5,5 3,4 B 4,2 2,3 L C R Game 2: T 0,4 5,-1 6,1 Pt M 5,-1 0,4 6,1 B |2,5 |2,5 |8,6
Some notes:
A hundred players are participating in this game (N 100). Each player has to choose an integer between 1 and 100 in order to guess "5/6 of the average of the responses given by all players". Each player who guesses the integer closest to the 5/6 of the average of all the responses, wins (a) Q4 Find all weakly dominated strategies (if any). (b) Find all strategies that survive the Iterative Elimination of Dominated Strategies (IEDS) (if any)...
Q1 Elimination of strictly-dominated strategies In each of the following two-player games, what strategies survive iterated elimination of strictly- dominated strategies? Player 2 Lett Center Right Top 0.2 4, 3 3,1 Player1 Middle 1, 2 2,0 2, Bottom 2,4 36 0,3 Player 2 Left Center Right Top 1, 3 ,4 ,2 Player 1 Middle 2,2 2 3,1 Bottom 3, 5 43 1, 4
Q1 Elimination of strictly-dominated strategies In each of the following two-player games, what strategies survive iterated elimination of strictly- dominated strategies? What are the Nash equilibria of these games? (a) Player 2 Left 0,2 1,3 2,4 Top Middle Bottom Center 4,3 2,4 1,5 Right 3, 4 2, 3 4,6 Player 1 (b) Player 2 Left 2,4 3,3 4,6 Top Middle Bottom Center 6,5 4,3 5,4 Player 1 Right 5,3 4, 2 2,5
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)...
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
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
Game Theory
Iterated Elimination: In the following normal-form game, which strategy profiles survive iterated elimination of strictly dominated strategies? 4.5 Player 2 L C R 6,8 2,6 8,2 Player 1 M 8,2 4,4 9,5 D 8,10 4,6 6,7
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...
(4) Using the Iterated elimination of (weakly) dominated strategy method, find all dom- inant strategy solutions of the following games P2 P2 L R Game 1: T 1,1 5,0 P M 5,5 3,4 B 4,2 2,3 L C R Game 2: T 0,4 5,-1 6,1 Pt M 5,-1 0,4 6,1 B |2,5 |2,5 |8,6
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