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8. Consider the two-player game described by the payoff matrix below. Player B L R Player...
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.
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...
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...
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.
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...
1. (60 marks) Consider a two-person game, in which every player has two pure strategies to...
1. (60 marks) Consider a two-person game, in which every player has two pure strategies to play. The payoff matrix of the game is as follows Strategy 2 Player One Player Two Strategy I Strategy II Strategy 1 0,0 1,3 1,1 Find all the Nash equilibria of the game.
2. Consider a static game described by the following payoff matrix: LR a,1 2,6 3,0 2,c...
2. Consider a static game described by the following payoff matrix: LR a,1 2,6 3,0 2,c B The two numbers in each cell is the payoffs to the row player and the column player, respectively. (a) [6] Find all parameter values of a, b, and c for which the strategy profile (T, L) is a weakly dominant strategy equilibrium. (b) [6] Find all parameter values of a, b, and c for which the strategy profile (T, L) is a pure...
Player lI A 6,6 2,0 В 0,1 а,а Player Consider the game represented above in which...
Player lI A 6,6 2,0 В 0,1 а,а Player Consider the game represented above in which BOTH Player 1 and Player 2 get a payoff of "a" when the strategy profile played is (B,D). Select the correct answer. If a-1 then strategy B is strictly dominated If a-3/2 then the game has two pure strategy Nash Equilibria. For all values of "a" strategy A is strictly dominant. For small enough values of "a", the profile (A,D) is a pure strategy...
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...
5. Consider the payoff matrix below, which shows two players each with three strategies. Player 2...
5. Consider the payoff matrix below, which shows two players each with three strategies. Player 2 A2 B2 C2 A1 20, 22 24, 20 25, 24 B1 23,26 21,24 22, 23 C1 19, 25 23,17 26,26 Player1 STUDENT NUMBER: SECTION: Page 11 of 12 pages Find all Nash equilibria in pure strategies for this simultaneous choice, one play game. Explain your reasoning. a) b) Draw the game in extended form and solve assuming sequential choice, with player 2 choosing first.
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.
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...
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...
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.
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...
1. (60 marks) Consider a two-person game, in which every player has two pure strategies to play. The payoff matrix of the game is as follows Strategy 2 Player One Player Two Strategy I Strategy II Strategy 1 0,0 1,3 1,1 Find all the Nash equilibria of the game.
2. Consider a static game described by the following payoff matrix: LR a,1 2,6 3,0 2,c B The two numbers in each cell is the payoffs to the row player and the column player, respectively. (a) [6] Find all parameter values of a, b, and c for which the strategy profile (T, L) is a weakly dominant strategy equilibrium. (b) [6] Find all parameter values of a, b, and c for which the strategy profile (T, L) is a pure...
Player lI A 6,6 2,0 В 0,1 а,а Player Consider the game represented above in which BOTH Player 1 and Player 2 get a payoff of "a" when the strategy profile played is (B,D). Select the correct answer. If a-1 then strategy B is strictly dominated If a-3/2 then the game has two pure strategy Nash Equilibria. For all values of "a" strategy A is strictly dominant. For small enough values of "a", the profile (A,D) is a pure strategy...
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...
5. Consider the payoff matrix below, which shows two players each with three strategies. Player 2 A2 B2 C2 A1 20, 22 24, 20 25, 24 B1 23,26 21,24 22, 23 C1 19, 25 23,17 26,26 Player1 STUDENT NUMBER: SECTION: Page 11 of 12 pages Find all Nash equilibria in pure strategies for this simultaneous choice, one play game. Explain your reasoning. a) b) Draw the game in extended form and solve assuming sequential choice, with player 2 choosing first.
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