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?
Homework Answers
(a)To find the best strategy for player A,( here row player) , find Maximum(ie., find minima of row and then select maximum of them) ie., strategy for row player is A2(Optimal/best)
Similarly, to find the best strategy for player B (here column player), find Minimax (i.e find maximum of column and then select minimum of them) ie., strategy for column player is B2 (optimal/best)
(b) Value of game to the colum player = 2
(saddle point(equilibrium point) iff Max(row min) = Min(column max))
(c)
PLayer A(row player) is favoured here because the value of game obtained is positive which shows gain for A. Had it been negative, B would've benefited.
Please leave a like. It'd help me so much. Thanks a lot.
Add Answer to:
Consider the following reward matrix for a two-person zero-sum
game:
9
0
6
3
2
4...
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
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.
1 -1 1 1/2 4. For the matrix game 5), compute the value, the optimal 1...
1 -1 1 1/2 4. For the matrix game 5), compute the value, the optimal 1 - 1 - 1 strategy for the row player, and two optimal strategies for the column player.
Q3 Three-Player Game Consider a 3-player matrix game. The correct interpretation is as follows: the row...
Q3 Three-Player Game Consider a 3-player matrix game. The correct interpretation is as follows: the row indicates which strategy was chosen by player I; the column indicates which strategy was chosen by player II. If player III chooses strategy X, then the three players' payoffs are given by the first matrix; if player III chooses strategy Y , then the three players' payoffs are given by the second matrix. II II LR 4, 7, 5 8, 1, 3 1, 1,8...
linear Algebra Find the optimal row and column strategies and the value of each matrix game. 4. a, A=[3 5 3 2 -1 91...
linear Algebra
Find the optimal row and column strategies and the value of each matrix game. 4. a, A=[3 5 3 2 -1 91 8 0 1 -1 43 b. A=11-1 3-1-3 2 -1 4 0 -2 -I 0-221」
Find the optimal row and column strategies and the value of each matrix game. 4. a, A=[3 5 3 2 -1 91 8 0 1 -1 43 b. A=11-1 3-1-3 2 -1 4 0 -2 -I 0-221」
For the 2 x 2 game, find the optimal strategy for each player. Be sure to check for saddle points before using the formulas. 9-3 For row player R: For column player C: Find the value v of the game fo...
For the 2 x 2 game, find the optimal strategy for each player. Be sure to check for saddle points before using the formulas. 9-3 For row player R: For column player C: Find the value v of the game for row plaver R. Who is the game favorable to? O The game is favorable to the row player. 0 The game is favorable to the column player. O This is a fair game.
For the 2 x 2 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
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...
For the game and mixed strategies, find the expected value. Let G=1 6 1 2 and...
For the game and mixed strategies, find the expected value. Let G=1 6 1 2 and c = مرا به راه را به 1-8 7 -6) For the game and mixed strategies, find the expected value. Let G = ( 8 3 -7 1, r = -4.6) and C= Un alw For the 2 x 2 game, find the optimal strategy for each player. Be sure to check for saddle points before using the formulas. For row player R: r1...
Copy of Copy of Consider the following matrix game M 5 Set up the minimization and...
Copy of Copy of Consider the following matrix game M 5 Set up the minimization and maximization linear programming problems for obtaining mixed strategies corresponding to row player and column player, respectively. DO NOT FIND the strategies.
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.
1 -1 1 1/2 4. For the matrix game 5), compute the value, the optimal 1 - 1 - 1 strategy for the row player, and two optimal strategies for the column player.
Q3 Three-Player Game Consider a 3-player matrix game. The correct interpretation is as follows: the row indicates which strategy was chosen by player I; the column indicates which strategy was chosen by player II. If player III chooses strategy X, then the three players' payoffs are given by the first matrix; if player III chooses strategy Y , then the three players' payoffs are given by the second matrix. II II LR 4, 7, 5 8, 1, 3 1, 1,8...
linear Algebra
Find the optimal row and column strategies and the value of each matrix game. 4. a, A=[3 5 3 2 -1 91 8 0 1 -1 43 b. A=11-1 3-1-3 2 -1 4 0 -2 -I 0-221」
Find the optimal row and column strategies and the value of each matrix game. 4. a, A=[3 5 3 2 -1 91 8 0 1 -1 43 b. A=11-1 3-1-3 2 -1 4 0 -2 -I 0-221」
For the 2 x 2 game, find the optimal strategy for each player. Be sure to check for saddle points before using the formulas. 9-3 For row player R: For column player C: Find the value v of the game for row plaver R. Who is the game favorable to? O The game is favorable to the row player. 0 The game is favorable to the column player. O This is a fair game.
For the 2 x 2 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
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...
For the game and mixed strategies, find the expected value. Let G=1 6 1 2 and c = مرا به راه را به 1-8 7 -6) For the game and mixed strategies, find the expected value. Let G = ( 8 3 -7 1, r = -4.6) and C= Un alw For the 2 x 2 game, find the optimal strategy for each player. Be sure to check for saddle points before using the formulas. For row player R: r1...
Copy of Copy of Consider the following matrix game M 5 Set up the minimization and maximization linear programming problems for obtaining mixed strategies corresponding to row player and column player, respectively. DO NOT FIND the strategies.
Most questions answered within 3 hours.
-
By 2025, annual consumption in emerging markets will total $30
trillion and contribute more than ________...
asked 3 minutes ago -
At what point does reformation cease to be a viable option for
those who are oppressed...
asked 7 minutes ago -
When rolling a die 129 times, what is the probability of rolling
a 6 no more...
asked 6 minutes ago -
Place letters corresponding to amounts in the proper order for
lightest to heaviest samples:
a) 2100...
asked 11 minutes ago -
Consider the multicore processor with 6 heterogeneous cores
labelled C1, C2, C3, C4, C5, and C6....
asked 14 minutes ago -
Document system components according to standards and procedures
(Implement and hand over system components) IT administrative
asked 14 minutes ago -
The college asked 700 students if they wanted a longer spring
break and 600 students said...
asked 14 minutes ago -
Determine the temperature (in Celsius) at which 1.00 mole of an
ideal gas will have a...
asked 38 minutes ago -
Japan’s combination of X and Y
Canada’s combination of X and Y
100x and 0y
50x...
asked 31 minutes ago -
[1] Household statistics include individuals living alone or in
groups in:
A) apartments.
B) military barracks....
asked 41 minutes ago -
What is the % w/v when 80 mL of a 2.0% solution is mixed with 50...
asked 45 minutes ago -
How can I solve the following using a TI83
Claim: Most adults would erase all of...
asked 58 minutes ago