Shown below is the solution to the linear program for finding Player A\'s optima

Question

Shown below is the solution to the linear program for finding Player A's optimal mixed strategy in a two-person, zero-sum game.

OBJECTIVE FUNCTION VALUE =     3.500

VARIABLE                           VALUE                                     REDUCED COSTS

PA1                                     0.050                                        0.000

PA2                                    0.600                                         0.000

PA3                                  0350                                            0.000

GAINA                               3.500                                            0.000

CONSTRAINT                       SLACK/SURPLUS                    DUAL PRICES

1                                              0.000                                      -0.500

2                                             0.000                                      -0.500

3                                             0.000                                       0.000

4                                            0.000 3.500

a.

What is Player A's optimal mixed strategy?

b.

What is Player B's optimal mixed strategy?

c.

What is Player A's expected gain?

d.

What is Player B's expected loss?

Kindly show all neccesary workings and provide me with citations in your narratives.

Explanation / Answer

Solution:

a. Player A's optimal mixedstrategy:Use strategyA1 with .05probability

Use strategyA2 with .60probability

Use strategyA3 with .35probability

b. Player B's optimal mixedstrategy:

Use strategyB1 with .50probability

Use strategyB2 with .50probability

Do not use strategyB3

c. Player A's expected gain: 3.500

d. Player B's expected loss: 3.500

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