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Exercise 2. Consider the following perfect information game: 1,1 0,0 0,0 (i) Solve the game using...
1. Consider the following extensive game: F G 2,1 3,1 0,2 2,3 (i) List all of...
1. Consider the following extensive game: F G 2,1 3,1 0,2 2,3 (i) List all of player 2's strategies. (2 points) (ii) Construct a payoff matrix and identify all Nash equilibria to the game. (2 points) (iii) Use backwards induction to find all subgame perfect equilibria of the game. (2 points)
2. Consider the following simultaneous move game: Column Left Right Top 1,1 7,3 Row Bottom 3,5...
2. Consider the following simultaneous move game: Column Left Right Top 1,1 7,3 Row Bottom 3,5 11,0 (a) Find all pure-strategy Nash equilibria (b) Now assume that the game is made sequential with Row moving first. Illustrate this new game using a game tree and find the rollback equilibrium (c) List the strategies of the two players in this sequential-move game and give the normal-form representation of the game (the payoff matrix) (d) Use the payoff matrix to find the...
2. Consider the following simultaneous move game: Column Left Right 1,1 3,5 11,0 Тoр 7,3 Row...
2. Consider the following simultaneous move game: Column Left Right 1,1 3,5 11,0 Тoр 7,3 Row Bottom (a) Find all pure-strategy Nash equilibria (b) Now assume that the game is made sequential with Row moving first. Illustrate this new game using a game tree and find the rollback equilibrium (c) List the strategies of the two players in this sequential-move game and give the normal-form representation of the game (the payoff matrix) (d) Use the payoff matrix to find the...
Q.2 Consider the following normal-form game: Player 2 Player 1 3,2 1,1 -1,3 R. 0,0 Q.2.a...
Q.2 Consider the following normal-form game: Player 2 Player 1 3,2 1,1 -1,3 R. 0,0 Q.2.a Identify the pure-strategy Nash equilibria. Q.2.b Identify the mixed-strategy Nash equilibria Q.2.c Calculate each player's expected equilibrium payoff.
1. Consider the following game in normal form. Player 1 is the "row" player with strate-...
1. Consider the following game in normal form. Player 1 is the "row" player with strate- gies a, b, c, d and Player 2 is the "column" player with strategies w, x, y, 2. The game is presented in the following matrix: a b c d w 3,3 1,1 0,0 0,0 x 2,1 1,2 1,0 0,5 y 0,2 1,0 3, 2 0,2 z 2,1 1,4 1,1 3,1 (a) Find the set of rationalizable strategies. (b) Find the set of Nash...
3. General Extensive Form Game D Suppose the following general extensive form game 1/2 1/2 (2,...
3. General Extensive Form Game D Suppose the following general extensive form game 1/2 1/2 (2, 2) (2, 2) (0, 6) (6, 0 (0,0 (6, 4) (a) Represent this game in normal form by using a matrix, and find all pure strategy Bayesian Nash equilibrium (equilibria) b) Find pure strategy subgame perfect equilibrium (or equilibria) of this game. c) Find pure strategy perfect Bayesian equilibrium (or equilibria) of this game.
1. Consider the following extensive form game with perfect information: 2 In 0 (a) (Level A)...
1. Consider the following extensive form game with perfect information: 2 In 0 (a) (Level A) Write down the normal form associated with this extensive formm game (b) (Level A) First suppose = 0. Find a subgame perfect equilibrium for this game. (c) (Level B) Again suppose α-0. Find a pure strategy Nash equilibrium of this extensive form game that is not subgame perfect. (d) (Level B) Now suppose α = 3. Find all pure strategy subgame perfect equi- libria....
2. Consider the following simultaneous move game Column Left Right 1.1 7,3 3.5 Тор Row Bottom...
2. Consider the following simultaneous move game Column Left Right 1.1 7,3 3.5 Тор Row Bottom 11.0 (a) Find all pure-strategy Nash equilibria. (b) Now assume that the game is made sequential with Row moving first. Illustrate this new game using a game tree and find the rollback equilibrium. (c) List the strategies of the two players in this sequential-move game and give the normal-form representation of the game (the payoff matrix) (d) Use the payoff matrix to find the...
Exercise 2 Consider the following simultaneous move game between two players I II III IV (-2,0)...
Exercise 2 Consider the following simultaneous move game between two players I II III IV (-2,0) (-1,0) (-1,1) C (0,1) (1,0) (0,2) (0,2) (0,2) A В (0,2) 1,2) (0,2) (0,2) (0,3) (0,4) (-1,3) (0,3) a. Use the Elimination of Weakly Dominated Strategies Criterion to obtain a solution (unique to the chosen order of elimination) b. Show that the order of elimination matters by finding a different solution (unique to the new chosen order of elimination) c. Show that the solutions...
1. Consider the following extensive form game with perfect information 1 Out 2 2 In 3...
1. Consider the following extensive form game with perfect information 1 Out 2 2 In 3 3 a) (Level A) Write down the normal form associated with this extensive form game (b) (Level A) First suppose -0. Find a subgame perfect equilibrium for this game (c) (Level B) Again suppose α-0. Find a pure strategy ash equilibrium of this extensive form game that is not subgame perfect (d) (Level B) Now suppose a-3. Find all pure strategy subgame perfect equi-...
1. Consider the following extensive game: F G 2,1 3,1 0,2 2,3 (i) List all of player 2's strategies. (2 points) (ii) Construct a payoff matrix and identify all Nash equilibria to the game. (2 points) (iii) Use backwards induction to find all subgame perfect equilibria of the game. (2 points)
2. Consider the following simultaneous move game: Column Left Right Top 1,1 7,3 Row Bottom 3,5 11,0 (a) Find all pure-strategy Nash equilibria (b) Now assume that the game is made sequential with Row moving first. Illustrate this new game using a game tree and find the rollback equilibrium (c) List the strategies of the two players in this sequential-move game and give the normal-form representation of the game (the payoff matrix) (d) Use the payoff matrix to find the...
2. Consider the following simultaneous move game: Column Left Right 1,1 3,5 11,0 Тoр 7,3 Row Bottom (a) Find all pure-strategy Nash equilibria (b) Now assume that the game is made sequential with Row moving first. Illustrate this new game using a game tree and find the rollback equilibrium (c) List the strategies of the two players in this sequential-move game and give the normal-form representation of the game (the payoff matrix) (d) Use the payoff matrix to find the...
Q.2 Consider the following normal-form game: Player 2 Player 1 3,2 1,1 -1,3 R. 0,0 Q.2.a Identify the pure-strategy Nash equilibria. Q.2.b Identify the mixed-strategy Nash equilibria Q.2.c Calculate each player's expected equilibrium payoff.
1. Consider the following game in normal form. Player 1 is the "row" player with strate- gies a, b, c, d and Player 2 is the "column" player with strategies w, x, y, 2. The game is presented in the following matrix: a b c d w 3,3 1,1 0,0 0,0 x 2,1 1,2 1,0 0,5 y 0,2 1,0 3, 2 0,2 z 2,1 1,4 1,1 3,1 (a) Find the set of rationalizable strategies. (b) Find the set of Nash...
3. General Extensive Form Game D Suppose the following general extensive form game 1/2 1/2 (2, 2) (2, 2) (0, 6) (6, 0 (0,0 (6, 4) (a) Represent this game in normal form by using a matrix, and find all pure strategy Bayesian Nash equilibrium (equilibria) b) Find pure strategy subgame perfect equilibrium (or equilibria) of this game. c) Find pure strategy perfect Bayesian equilibrium (or equilibria) of this game.
1. Consider the following extensive form game with perfect information: 2 In 0 (a) (Level A) Write down the normal form associated with this extensive formm game (b) (Level A) First suppose = 0. Find a subgame perfect equilibrium for this game. (c) (Level B) Again suppose α-0. Find a pure strategy Nash equilibrium of this extensive form game that is not subgame perfect. (d) (Level B) Now suppose α = 3. Find all pure strategy subgame perfect equi- libria....
2. Consider the following simultaneous move game Column Left Right 1.1 7,3 3.5 Тор Row Bottom 11.0 (a) Find all pure-strategy Nash equilibria. (b) Now assume that the game is made sequential with Row moving first. Illustrate this new game using a game tree and find the rollback equilibrium. (c) List the strategies of the two players in this sequential-move game and give the normal-form representation of the game (the payoff matrix) (d) Use the payoff matrix to find the...
Exercise 2 Consider the following simultaneous move game between two players I II III IV (-2,0) (-1,0) (-1,1) C (0,1) (1,0) (0,2) (0,2) (0,2) A В (0,2) 1,2) (0,2) (0,2) (0,3) (0,4) (-1,3) (0,3) a. Use the Elimination of Weakly Dominated Strategies Criterion to obtain a solution (unique to the chosen order of elimination) b. Show that the order of elimination matters by finding a different solution (unique to the new chosen order of elimination) c. Show that the solutions...
1. Consider the following extensive form game with perfect information 1 Out 2 2 In 3 3 a) (Level A) Write down the normal form associated with this extensive form game (b) (Level A) First suppose -0. Find a subgame perfect equilibrium for this game (c) (Level B) Again suppose α-0. Find a pure strategy ash equilibrium of this extensive form game that is not subgame perfect (d) (Level B) Now suppose a-3. Find all pure strategy subgame perfect equi-...
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