Explanation Given: The payoff matrix of a game is given by, [ 2 5 3 − 6 ] Approach: Let [ a b c d ] be the payoff matrix for a non-strictly determined game. Then the optional mixed strategy for the row player is given by P = [ p 1 p 2 ] Where, p 1 = d − c a + d − b − c p 2 = 1 − p 1 And the optimal mixed strategy for the column player is given by, Q = [ q 1 q 2 ] Where, q 1 = d − b a + d − b − c q 2 = 1 − q 1 Furthermore, the value of the game is given by the expected value of the game, E = P A Q , where P and Q are the optional mixed strategies for the row and column players, respectively. Thus, E = P A Q = a d − b c a + d − b − c Calculation: Compare the given matrix with a standard payoff matrix. a = 2 b = 5 c = 3 d = − 6 Write the expression to calculate the first term of optional mixed strategy for the row. p 1 = d − c a + d − b − c Substitute 2 for a , 5 for b , 3 for c and − 6 for d in the above expression. p 1 = − 6 − 3 2 − 6 − 5 − 3 = − 9 12 = − 3 4 Write the expression to calculate the second term of optional mixed strategy for the row. p 2 = 1 − p 1 Substitute − 3 4 for p 1 in the above expression. p 2 = 1 − ( − 3 4 ) = 4 + 3 4 = 7 4 Write the expression for the optional mixed strategy for the row. P = [ p 1 p 2 ] Substitute − 3 4 for p 1 and 7 4 for p 2 in the above expression. P = [ − 3 4 7 4 ] Write the expression to calculate the first term of optional mixed strategy for the column

11th Edition

ISBN: 9781337496094

Author: Tan

Publisher: CENGAGE C

See similar textbooks

Videos

Question

Chapter 9.5, Problem 12E

To determine

To find:

The optimal strategies P and Q for the row and column players and expected payoff E of each matrix game.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.5, Problem 11E

Chapter 9.5, Problem 13E

Students have asked these similar questions

Find the optimal strategies, P and Q, for the row and column players, respectively. P= Q= 8 Compute the expected payoff E of the matrix game if the players use their optimal strategies. (Round your answer to two decimal places.) E = 2 Which player does the game favor, if any? OR OC neither

Find the optimal strategies, P and Q, for the row and column players, respectively. р Compute the expected payoff E of the matrix game if the players use their optimal strategies. (Round your answer to two decimal places.) 6- Which player does the game favor, if any? OR Oc O neither

Find the optimal strategies, P and Q, for the row and column players, respectively. −2 −5 −8 −4 P = Q = Compute the expected payoff E of the matrix game if the players use their optimal strategies. (Round your answer to two decimal places.)E =

Chapter 9 Solutions

FINITE MATH.F/MGRL....(LL)>CUSTOM PKG.<

Ch. 9.1 - What is a finite stochastic process? What can you...Ch. 9.1 - Prob. 2CQ Ch. 9.1 - Consider a transition matrix T for a Markov chain...Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The optimal strategies P and Q for the row and column players and expected payoff E of each matrix game.

Solution Summary: The author explains the optimal strategies P and Q for the row and column players and expected payoff E of each matrix game.

Videos

To find: The optimal strategies P and Q for the row and column players and expected payoff E of each matrix game.

Want to see the full answer?

Chapter 9 Solutions

To find:

The optimal strategies P and Q for the row and column players and expected payoff E of each matrix game.