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Player lI A 6,6 2,0 В 0,1 а,а Player Consider the game represented above in which...
Player Il Player lI Player lI A 2,3,1 3,1,0 В 3,2,11,32 Player I A 1,3,3 -1,3,2...
Player Il Player lI Player lI A 2,3,1 3,1,0 В 3,2,11,32 Player I A 1,3,3 -1,3,2 Player l В 3,1,0 0,0,4 The game above is a simultaneous three player game between players 1, 2, and 3. Player 1 chooses between A and B, Player 2 between C and D and Player 3 between E and F. In the game above, the strategy profile in which Player 1 plays and Player 3 plays Player 2 plays is a Nash Equilibrium profile.
8. Consider the two-player game described by the payoff matrix below. Player B L R Player...
8. Consider the two-player game described by the payoff matrix below. Player B L R Player A D 0,0 4,4 (a) Find all pure-strategy Nash equilibria for this game. (b) This game also has a mixed-strategy Nash equilibrium; find the probabilities the players use in this equilibrium, together with an explanation for your answer (c) Keeping in mind Schelling's focal point idea from Chapter 6, what equilibrium do you think is the best prediction of how the game will be...
GAME MATRIX Consider two players (Rose as player 1 and Kalum as player 2) in which each player has 2 possible actions (...
GAME MATRIX
Consider two players (Rose as player 1 and Kalum as player 2) in which each player has 2 possible actions (Up or Down for Rose; Left or Right for Kalum. This can be represented by a 2x2 game with 8 different numbers (the payoffs). Write out three different games such that: (a) There are zero pure-strategy Nash equilibria. (b) There is exactly one pure-strategy equilibrium. (c) There are two pure-strategy Nash equilibria.
Consider two players (Rose as player...
Player lI C D E A 0,0 0,2 2,1 В 1,2 1,1 0,0 Player B Consider...
Player lI C D E A 0,0 0,2 2,1 В 1,2 1,1 0,0 Player B Consider the strategic form game above and select all that apply. Strategy A is not dominant for Player 1. Strategy B is weakly dominant for player I. Strategy E is dominated by strategies C and D for player 2. Strategy E is never a best response.
3. Consider the following two-player game in strategic form LM R A 2,2 2,2 2,2 В 3,3 0,2 0,0 С 0,...
3. Consider the following two-player game in strategic form LM R A 2,2 2,2 2,2 В 3,3 0,2 0,0 С 0,0 3,2 0,3 This game will demonstrate several methods for ruling out possible mixed- strategy equilibria (a) What are the pure strategy equilibria? (b) Show that there does not exist an equilibrium in which Player 1 (the row player) assigns strictly positive probability to A, to B, and to C. (c) Show that there does not exist an equilibrium in...
Consider the following simultaneous game: Player 2 L R Player 1 U 30,20 -10-10 D -10-10...
Consider the following simultaneous game: Player 2 L R Player 1 U 30,20 -10-10 D -10-10 20.30 Please indicate whether each of the following statements is true or false. Player 1 has a dominant strategy. This game has two Nash equilibria in pure strategies. Player 1's payoff in each of the Nash equilibria is 30.
Consider the following extensive-form game with two players, 1 and 2. a). Find the pure-strategy Nash...
Consider the following extensive-form game with two players, 1
and 2.
a). Find the pure-strategy Nash equilibria of the game. [8
Marks]
b). Find the pure-strategy subgame-perfect equilibria of the
game. [6 Marks]
c). Derive the mixed strategy Nash equilibrium of the subgame.
If players play this mixed Nash equilibrium in the subgame, would 1
player In or Out at the initial mode? [6 Marks]
[Hint: Write down the normal-form of the subgame and derive the
mixed Nash equilibrium of...
Consider the voluntary contribution to building a fence game discussed in class. Assume that v1-v2-100 and...
Consider the voluntary contribution to building a fence game discussed in class. Assume that v1-v2-100 and C=150, and select all that apply a. There are Nash equilibria in which the fence is not built. D. It is efficient to build the fence. .Contributing more than her own valuation is a strictly dominated strategy for each player. d. Each player donating 100 is a pure strategy Nash equilibrium in the game.
(2,5). Find the Walrasian equilibrium. 4. 120] Answer the following. (a) 14 Explain the difference between...
(2,5). Find the Walrasian equilibrium. 4. 120] Answer the following. (a) 14 Explain the difference between a strategy that is a best response versus a strategy that is strictly dominant. (b) (6) Consider the following game: player 2 D E F C A 3,7 7,3 1,2 4,3 player 1 B 8,9 8,5 2,8 5,2 C 0,10 7,01,9 2,2 Find the strictly dominant strategies solution and the iterated elimination of strictly dominated strategies solution, if any. (c) [10] Consider the following...
Consider the voluntary contribution to building a fence game discussed in class. Assume that v1 =...
Consider the voluntary contribution to building a fence game discussed in class. Assume that v1 = v2=100 and C=150, and select all that apply. a. It is efficient to build the fence. b. Contributing more than her own valuation is a strictly dominated strategy for each player. c. Each player donating 100 is a pure strategy Nash equilibrium in the game. d. There are Nash equilibria in which the fence is not built.
Player Il Player lI Player lI A 2,3,1 3,1,0 В 3,2,11,32 Player I A 1,3,3 -1,3,2 Player l В 3,1,0 0,0,4 The game above is a simultaneous three player game between players 1, 2, and 3. Player 1 chooses between A and B, Player 2 between C and D and Player 3 between E and F. In the game above, the strategy profile in which Player 1 plays and Player 3 plays Player 2 plays is a Nash Equilibrium profile.
8. Consider the two-player game described by the payoff matrix below. Player B L R Player A D 0,0 4,4 (a) Find all pure-strategy Nash equilibria for this game. (b) This game also has a mixed-strategy Nash equilibrium; find the probabilities the players use in this equilibrium, together with an explanation for your answer (c) Keeping in mind Schelling's focal point idea from Chapter 6, what equilibrium do you think is the best prediction of how the game will be...
GAME MATRIX
Consider two players (Rose as player 1 and Kalum as player 2) in which each player has 2 possible actions (Up or Down for Rose; Left or Right for Kalum. This can be represented by a 2x2 game with 8 different numbers (the payoffs). Write out three different games such that: (a) There are zero pure-strategy Nash equilibria. (b) There is exactly one pure-strategy equilibrium. (c) There are two pure-strategy Nash equilibria.
Consider two players (Rose as player...
Player lI C D E A 0,0 0,2 2,1 В 1,2 1,1 0,0 Player B Consider the strategic form game above and select all that apply. Strategy A is not dominant for Player 1. Strategy B is weakly dominant for player I. Strategy E is dominated by strategies C and D for player 2. Strategy E is never a best response.
3. Consider the following two-player game in strategic form LM R A 2,2 2,2 2,2 В 3,3 0,2 0,0 С 0,0 3,2 0,3 This game will demonstrate several methods for ruling out possible mixed- strategy equilibria (a) What are the pure strategy equilibria? (b) Show that there does not exist an equilibrium in which Player 1 (the row player) assigns strictly positive probability to A, to B, and to C. (c) Show that there does not exist an equilibrium in...
Consider the following simultaneous game: Player 2 L R Player 1 U 30,20 -10-10 D -10-10 20.30 Please indicate whether each of the following statements is true or false. Player 1 has a dominant strategy. This game has two Nash equilibria in pure strategies. Player 1's payoff in each of the Nash equilibria is 30.
Consider the following extensive-form game with two players, 1
and 2.
a). Find the pure-strategy Nash equilibria of the game. [8
Marks]
b). Find the pure-strategy subgame-perfect equilibria of the
game. [6 Marks]
c). Derive the mixed strategy Nash equilibrium of the subgame.
If players play this mixed Nash equilibrium in the subgame, would 1
player In or Out at the initial mode? [6 Marks]
[Hint: Write down the normal-form of the subgame and derive the
mixed Nash equilibrium of...
Consider the voluntary contribution to building a fence game discussed in class. Assume that v1-v2-100 and C=150, and select all that apply a. There are Nash equilibria in which the fence is not built. D. It is efficient to build the fence. .Contributing more than her own valuation is a strictly dominated strategy for each player. d. Each player donating 100 is a pure strategy Nash equilibrium in the game.
(2,5). Find the Walrasian equilibrium. 4. 120] Answer the following. (a) 14 Explain the difference between a strategy that is a best response versus a strategy that is strictly dominant. (b) (6) Consider the following game: player 2 D E F C A 3,7 7,3 1,2 4,3 player 1 B 8,9 8,5 2,8 5,2 C 0,10 7,01,9 2,2 Find the strictly dominant strategies solution and the iterated elimination of strictly dominated strategies solution, if any. (c) [10] Consider the following...
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