Homework Answers
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For player 1, strategy D dominates strategy U (since 4>3 (i.e, payoff of player 1 when (U,L) is played) and 0>-1 (i.e, payoff of player 1 when (U,R) is played)). So, we can eliminate startegy U and thus player 1 never plays U;
So, when Player 1 plays D, player 2 plays R (since 0>-1(i.e, the payoff from L)). So, (D,R) is the equilibrium where player 1 gets a payoff of 0 and player 2 also gets a payoff of 0.
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Consider the following payoff matrix L R U 3,3 -1,2 D 4,-1 0,0 If Player 1...
1 pts Question 8 U Player 2 L R U 2.0 2,1 Player 1 D 3,1...
1 pts Question 8 U Player 2 L R U 2.0 2,1 Player 1 D 3,1 1,2 The above figure shows the payoff matrix for two players, Player 1 and Player 2. Player 1's payoff is listed first in each cell. A Nash equilibrium of this game is that Player 1 chooses and Player 2 chooses L. Player 1 chooses and Player 2 chooses R. Player 1 chooses and Player 2 chooses L. Player 1 chooses U and Player 2...
2. (25 pts) Consider a two player game with a payoff matrix (1)/(2) L U D...
2. (25 pts) Consider a two player game with a payoff matrix (1)/(2) L U D R (2,1) (1,0) (0,0) (3,-4) where e E{-1,1} is a parameter known by player 2 only. Player 1 believes that 0 = 1 with probability 1/2 and 0 = -1 with probability 1/2. Everything above is common knowledge. (a) Write down the strategy space of each player. (b) Find the set of pure strategy Bayesian Nash equilibria.
Player II A 2,6 0A 4A В 3,3 0,0 1,5 С 1,1 3,5 2,3 Player Consider...
Player II A 2,6 0A 4A В 3,3 0,0 1,5 С 1,1 3,5 2,3 Player Consider the strategic form game above. The number of strategies player 1 has is and player 2 moves at information sets (Please write numerical values like 0,1, 74, etc.)
8. Consider the two-player game described by the payoff matrix below. Player B L R Player...
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Player 2 L R U 2,1 2,0 Player 1 D 1, 2 3, 1 The above figure shows the payoff matrix for two players, Player 1 and Player 2. Player 1's payoff is listed first in each cell. A Nash equilibrium of this game is that Player 1 chooses D and Player 2 chooses L. Player 1 chooses D and Player 2 chooses R. Player 1 chooses U and Player 2 chooses L. Player 1 chooses U and Player 2...
The following matrix gives the payoff for Player 1 and Player 2 with R and L...
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1. Consider a gaine where the row player moves first, choosing between T and B. The...
1. Consider a gaine where the row player moves first, choosing between T and B. The column player observes the row player's action and must choose between L and R. In the payoff table given in (a), solve for the unique backward induction strategy profile, and compare it to the Nash equilibrium when actions are chosen simultaneously. In the payoff table (b); solve for all pure strategy Nash equilibria. Optional question: Are there any inixed strategy equilibria in (b)? DLR...
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...
stion 4 10 points Save Answer Player II С 6,6 1,7 D 7,1 3,3 Player l...
stion 4 10 points Save Answer Player II С 6,6 1,7 D 7,1 3,3 Player l Consider a game in which Player 1 first selects between L and R. f Player 1 selects L, then players 1 and 2 play a prisoner's dlemma game represented in the strategic form above it Player 1 selects R then, Player 1 and 2 play the battie-of the-sexes game in which they simultaneously and independently choose between A and B. If they both choose...
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In the extensive form representation of the game between Player 1 and Player 2, Player 1 moves first and chooses L or R. If Player 1 chooses R the game ends, if Player 1 chooses L then Player 1 and 2 play a simultaneous move game. The game has______________ pure strategy Nash equilibria and__________ pure strategy Subgame Perfect Nash Equilibria (SPNE). The maximum payoff Player 2 gets in a SPNE is___________ . (Please, enter only numerical answers like: 1, 2,...
1 pts Question 8 U Player 2 L R U 2.0 2,1 Player 1 D 3,1 1,2 The above figure shows the payoff matrix for two players, Player 1 and Player 2. Player 1's payoff is listed first in each cell. A Nash equilibrium of this game is that Player 1 chooses and Player 2 chooses L. Player 1 chooses and Player 2 chooses R. Player 1 chooses and Player 2 chooses L. Player 1 chooses U and Player 2...
2. (25 pts) Consider a two player game with a payoff matrix (1)/(2) L U D R (2,1) (1,0) (0,0) (3,-4) where e E{-1,1} is a parameter known by player 2 only. Player 1 believes that 0 = 1 with probability 1/2 and 0 = -1 with probability 1/2. Everything above is common knowledge. (a) Write down the strategy space of each player. (b) Find the set of pure strategy Bayesian Nash equilibria.
Player II A 2,6 0A 4A В 3,3 0,0 1,5 С 1,1 3,5 2,3 Player Consider the strategic form game above. The number of strategies player 1 has is and player 2 moves at information sets (Please write numerical values like 0,1, 74, etc.)
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stion 4 10 points Save Answer Player II С 6,6 1,7 D 7,1 3,3 Player l Consider a game in which Player 1 first selects between L and R. f Player 1 selects L, then players 1 and 2 play a prisoner's dlemma game represented in the strategic form above it Player 1 selects R then, Player 1 and 2 play the battie-of the-sexes game in which they simultaneously and independently choose between A and B. If they both choose...
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