Homework Answers
Game 1: There is no pure Nash equilibrium as there are no strictly dominated strategies for both the players. Also, there is no mixed strategy Nash equilibrium as the probability for playing R for a player 2 is negative (image attached).
Each player is assigned a probability to play a particular
strategy. Given the other player's probability to play a particular
strategy they maximize their expected pay-off.
Game 2: There is no pure Nash equilibrium as there are no strictly dominated strategies for both the players. Also, there is no mixed strategy Nash equilibrium as there is no specific probability for player 2 can be derived (image attached).
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Question 2. (100/3 pts.) Find the mixed strategy best responses to the following games (while not...
Determine ALL of the Nash equilibria (pure-strategy and mixed-strategy equilibria) of the following 3 games: Player...
Determine ALL of the Nash equilibria
(pure-strategy and mixed-strategy equilibria) of
the following 3 games:
Player 1 H T Player 2 HT (1, -1) (-1,1) | (-1,1) (1, -1) | Н Player 1 H D Player 2 D (2, 2) (3,1) | (3,1) |(2,2) | Player 2 A (2, 2) (0,0) Player 1 A B B (0,0) | (3,4)
4. Compute the mixed-strategy equilibria of the following games. 1 А в \ L M R...
4. Compute the mixed-strategy equilibria of the following games. 1 А в \ L M R 2,4 0,0 3. 6,3 | 3,5 5,5 B 1,6 | 3,7 4,8 5,2 | 3,7 4,9
4. [20] Answer the following. (a) (5) State the relationship between strictly dominant strategies solution and...
4. [20] Answer the following. (a) (5) State the relationship between strictly dominant strategies solution and iterated elimination of strictly dominated strategies solution. That is, does one solution concept imply the other? (b) (5) Consider the following game: player 2 E F G H A-10,6 10.0 3,8 4.-5 player 1 B 9,8 14,8 4.10 2,5 C-10,3 5,9 8.10 5,7 D 0,0 3,10 8,12 0,8 Does any player have a strictly dominant strategies? Find the strictly dominant strategies solution and the...
#2. Find all pure and mixed strategy Nash equilibria (if any) in the following game. U...
#2. Find all pure and mixed strategy Nash equilibria (if any) in the following game. U 1,1 0,0 0, -1 S 0,0 1,1 0, -1 D.0.0 0,-1
3. (30 pts) Consider the following game. Players can choose either left () or 'right' (r) The tab...
3. (30 pts) Consider the following game. Players can choose either left () or 'right' (r) The table provided below gives the payoffs to player A and B given any set of choices, where player A's payoff is the firat number and player B's payoff is the second number Player B Player A 4,4 1,6 r 6,1 -3.-3 (a) Solve for the pure strategy Nash equilibria. (4 pta) (b) Suppose player A chooses l with probability p and player B...
Find all pure strategy Nash Equilibria in the following games a.) Player 2 b1 b2...
Find all pure strategy Nash Equilibria in the following games a.) Player 2 b1 b2 b3 a1 1,3 2,2 1,2 a2 2,3 2,3 2,1 a3 1,1 1,2 3,2 a4 1,2 3,1 2,3 Player 1 b.) Player 2 A B C D A 1,3 3,1 0,2 1,1 B 1,2 1,2 2,3 1,1 C 3,2 2,1 1,3 0,3 D 2,0 3,0 1,1 2,2 Player 1 c.) Player 2 S B S 3,2 1,1 B 0,0 2,3
microecon 1 Static games (9 pts.) For each of the following games: Circle all payoffs corresponding...
microecon
1 Static games (9 pts.) For each of the following games: Circle all payoffs corresponding to a player's best response. Identify any/all strictly dominant strategies (or indicate that there are none). Identify any/all strictly dominated strategies (or indicate that there are none). Identify any/all pure strategy Nash equilibria by writing the equilibrium strategies as an ordered pair. (If there is no PSNE, write "no PSNE".) a. (3 pts.) Two friends are deciding what costumes to wear for Halloween. Matt...
1. Assuming all players use pure strategies, describe the best response strategy for each player and...
1. Assuming all players use pure strategies, describe the best response strategy for each player and determine the pure strategy Nash Equilibrium for each of the following games. a) Coordination Game: In such games the two players benefit from coordinating their actions. The "Prisoner's Dilemma" game we studied in class was an example of such coordination game. Here is another example known as "Battle of the Sexes." In this game a husband and wife trying to decide how they should...
3. [20] Consider an Edgeworth box economy are given by (a) [5) Find all the Pareto...
3. [20] Consider an Edgeworth box economy are given by (a) [5) Find all the Pareto optimal allocations. sing the normalization, P2 = 1, find the Walrasian equilibrium. ully state the first welfare theorem and verify that it holds. dowments had instead been ē1 = (18,15) and (d) [5] Suppose the en = (2,5). Find the Walrasian equilibrium. 4. [20] Answer the following. (a) [4] Explain the difference between a strategy that is a best response versus a strategy that...
For each of the following normal-form game below, find the rationalizable strategy profiles, using IENBRS, Iterated...
For each of the following normal-form game below, find the rationalizable strategy profiles, using IENBRS, Iterated Elimination of Never a Best Response Strategies. (1)/(2) L C R (3,2) (4,0) (1,1) (2,0) (3,3) (0,0) (1,1) (0,2) (2,3)
Determine ALL of the Nash equilibria
(pure-strategy and mixed-strategy equilibria) of
the following 3 games:
Player 1 H T Player 2 HT (1, -1) (-1,1) | (-1,1) (1, -1) | Н Player 1 H D Player 2 D (2, 2) (3,1) | (3,1) |(2,2) | Player 2 A (2, 2) (0,0) Player 1 A B B (0,0) | (3,4)
4. Compute the mixed-strategy equilibria of the following games. 1 А в \ L M R 2,4 0,0 3. 6,3 | 3,5 5,5 B 1,6 | 3,7 4,8 5,2 | 3,7 4,9
4. [20] Answer the following. (a) (5) State the relationship between strictly dominant strategies solution and iterated elimination of strictly dominated strategies solution. That is, does one solution concept imply the other? (b) (5) Consider the following game: player 2 E F G H A-10,6 10.0 3,8 4.-5 player 1 B 9,8 14,8 4.10 2,5 C-10,3 5,9 8.10 5,7 D 0,0 3,10 8,12 0,8 Does any player have a strictly dominant strategies? Find the strictly dominant strategies solution and the...
#2. Find all pure and mixed strategy Nash equilibria (if any) in the following game. U 1,1 0,0 0, -1 S 0,0 1,1 0, -1 D.0.0 0,-1
3. (30 pts) Consider the following game. Players can choose either left () or 'right' (r) The table provided below gives the payoffs to player A and B given any set of choices, where player A's payoff is the firat number and player B's payoff is the second number Player B Player A 4,4 1,6 r 6,1 -3.-3 (a) Solve for the pure strategy Nash equilibria. (4 pta) (b) Suppose player A chooses l with probability p and player B...
microecon
1 Static games (9 pts.) For each of the following games: Circle all payoffs corresponding to a player's best response. Identify any/all strictly dominant strategies (or indicate that there are none). Identify any/all strictly dominated strategies (or indicate that there are none). Identify any/all pure strategy Nash equilibria by writing the equilibrium strategies as an ordered pair. (If there is no PSNE, write "no PSNE".) a. (3 pts.) Two friends are deciding what costumes to wear for Halloween. Matt...
1. Assuming all players use pure strategies, describe the best response strategy for each player and determine the pure strategy Nash Equilibrium for each of the following games. a) Coordination Game: In such games the two players benefit from coordinating their actions. The "Prisoner's Dilemma" game we studied in class was an example of such coordination game. Here is another example known as "Battle of the Sexes." In this game a husband and wife trying to decide how they should...
3. [20] Consider an Edgeworth box economy are given by (a) [5) Find all the Pareto optimal allocations. sing the normalization, P2 = 1, find the Walrasian equilibrium. ully state the first welfare theorem and verify that it holds. dowments had instead been ē1 = (18,15) and (d) [5] Suppose the en = (2,5). Find the Walrasian equilibrium. 4. [20] Answer the following. (a) [4] Explain the difference between a strategy that is a best response versus a strategy that...
For each of the following normal-form game below, find the rationalizable strategy profiles, using IENBRS, Iterated Elimination of Never a Best Response Strategies. (1)/(2) L C R (3,2) (4,0) (1,1) (2,0) (3,3) (0,0) (1,1) (0,2) (2,3)
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