4. Consider the following two-person zero-sum game. Assume the two players have the same two strategy...
4. Consider the following two-person zero-sum game. Assume the two players have the same two strategy options. The payoff table shows the gains for Player A. Player B. Determine the optimal strategy for each player. What is the value of the game?
|
Player B |
||
|
Player A |
Strategy b1 |
Strategy b2 |
|
Strategy a1 |
3 |
9 |
|
Strategy a2 |
6 |
2 |
Homework Answers
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4. Consider the following two-person zero-sum game. Assume the
two players have the same two strategy...
Consider the two-person, zero-sum game having the following payoff table. Player 2 Strategy نیا نیا Player...
Consider the two-person, zero-sum game having the following payoff table. Player 2 Strategy نیا نیا Player 1 یہ نم دیا با را (a) Assuming this is a stable game, use the minimax (or maximin) criterion to determine the best strategy for each player. Does this game have a saddle point? If so, identify it. Is this a stable game?
11. Consider the two-person, zero-sum game having the following payoff table for Player A S1 89...
11. Consider the two-person, zero-sum game having the following payoff table for Player A S1 89 13 S2 15 13 8 S 14 157 (a) Does this game have a saddle point? If so, identify it. (b) Formulate the problem of finding the optimal strategy for Player A according to the maximin criterion as a linear programming problem. Explain the interpretation of your decision variables
Consider the following reward matrix for a two-person zero-sum game: 9 0 6 3 2 4...
Consider the following reward matrix for a two-person zero-sum game: 9 0 6 3 2 4 3 1 5 (a) Find optimal strategies for both the row and column players. (b) What is the value of the game to the column player?. (c) Who is favoured by the game?
Consider the competitive, static, one-time game depicted in the following figure. If larger payoffs are preferred,...
Consider the competitive, static, one-time game depicted in the following figure. If larger payoffs are preferred, does either player have a dominant strategy? If B believes that A will move A1, how should B move? If B believes that A will move A2, how should B move? What is the Nash equilibrium strategy profile if this game is played just once? What is the strategy profile for this game if both players adopt a secure strategy? What strategy profile results...
Consider the following two player game. The players’ strategy spaces are SA = {a1, a2, a3}...
Consider the following two player game. The players’ strategy
spaces are SA = {a1, a2, a3} and SB = {b1, b2, b3, b4}.
(d) Derive all the rationalizable strategy profiles.
(e) Derive the players’ best reply correspondences.
(f) Compute all the Nash equilibria of the game
A\В by 2, 2 3, 1 8,0 3, 6 а1 3, 1 0, 6 1, 4 1, 0 а2 4, 2 1, 1 2, 2 4, 4 аз
A\В by 2, 2 3, 1...
A two-player zero sum game in which [Si] = n for i = 1, 2 is...
A two-player zero sum game in which [Si] = n for i = 1, 2 is called symmetric if A, the payoff matrix for Player 1 satisfies A = -AT. (a) In linear algebra, how do we classify A when A = -AT? (b) Does this definition of symmetric match the traditional definition of a symmetric game? Explain. (c) Suppose x is an optimal maximin strategy for Player 1 in a symmetric zero-sum game. Prove x is an optimal maximin...
Find the row player's optimal strategy r = 21, x2]" in the two-person zero-sum game with...
Find the row player's optimal strategy r = 21, x2]" in the two-person zero-sum game with the payoff matrix A being given by A= (4 5 1 (216 x1 + x2=1, 21 > 0, and x2 > 0.
QUESTION 8 Consider a game with two players, players and player 2. Player 1's strategies are...
QUESTION 8 Consider a game with two players, players and player 2. Player 1's strategies are up and down, and player 2's strategies are left and right. Suppose that player 1's payoff function is such that for any combination of the players chosen strategies, player 1 always receives a payoff equal to 0. Suppose further that player 2's payoff function is such that no two combinations of the players' chosen strategies ever give player 2 the same payoff Choose the...
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.
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 two-person, zero-sum game having the following payoff table. Player 2 Strategy نیا نیا Player 1 یہ نم دیا با را (a) Assuming this is a stable game, use the minimax (or maximin) criterion to determine the best strategy for each player. Does this game have a saddle point? If so, identify it. Is this a stable game?
11. Consider the two-person, zero-sum game having the following payoff table for Player A S1 89 13 S2 15 13 8 S 14 157 (a) Does this game have a saddle point? If so, identify it. (b) Formulate the problem of finding the optimal strategy for Player A according to the maximin criterion as a linear programming problem. Explain the interpretation of your decision variables
Consider the following two player game. The players’ strategy
spaces are SA = {a1, a2, a3} and SB = {b1, b2, b3, b4}.
(d) Derive all the rationalizable strategy profiles.
(e) Derive the players’ best reply correspondences.
(f) Compute all the Nash equilibria of the game
A\В by 2, 2 3, 1 8,0 3, 6 а1 3, 1 0, 6 1, 4 1, 0 а2 4, 2 1, 1 2, 2 4, 4 аз
A\В by 2, 2 3, 1...
A two-player zero sum game in which [Si] = n for i = 1, 2 is called symmetric if A, the payoff matrix for Player 1 satisfies A = -AT. (a) In linear algebra, how do we classify A when A = -AT? (b) Does this definition of symmetric match the traditional definition of a symmetric game? Explain. (c) Suppose x is an optimal maximin strategy for Player 1 in a symmetric zero-sum game. Prove x is an optimal maximin...
Find the row player's optimal strategy r = 21, x2]" in the two-person zero-sum game with the payoff matrix A being given by A= (4 5 1 (216 x1 + x2=1, 21 > 0, and x2 > 0.
QUESTION 8 Consider a game with two players, players and player 2. Player 1's strategies are up and down, and player 2's strategies are left and right. Suppose that player 1's payoff function is such that for any combination of the players chosen strategies, player 1 always receives a payoff equal to 0. Suppose further that player 2's payoff function is such that no two combinations of the players' chosen strategies ever give player 2 the same payoff Choose the...
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.
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...
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