Fenton and Farrah Friendly, husband - and - wife car dealers, are soon going to

Question

Fenton and Farrah Friendly, husband - and - wife car dealers, are soon going to open a new dealership. They have three offers: from a foreign compact car company, from a U.S. producer of full - sized cars, and from a truck company. The success of each type of dealership will depend on how much gasoline is going to be available during the next few years. The profit from each type of dealership, given the availability of gas, is shown in the following payoff table:

Degree Program Graphic design Nursing Real estate Medical technology Culinary technology Computer information Maximax decision Maximin decision Economic Conditions Good Recession Average Robust Maximum Minimum Summary Decision 175,000 150,000 220,000 200,000 220,000 150,000 Real estate 215.000 215.000 160.000 b) maximin Nursing 160,000 180,000 205,000 220,000 210,000 220,000 125.000 165,000 125,000 c) equal likelihood Real estate 210,000 270,000 270,000 135,000 d Hurwicz (alpha E 0 135,000 180,000 Real estate 235,000 205,000 235.000 110.000 110,000 145,000 130,000 150,000 190,000 245,000 245,000 130,000

Explanation / Answer

FROM FIRST TABLE

MAXIMAX DECISION VALUE = 270,000 (OBTAINED FROM "MAXIMUM" HEADED COLUMN)

MAXIMIN DECISION VALUE = 160,000 (THIS IS NOT EQUAL TO MINIMAX VALUE=215,000) SO SADDLE POINT DOES NOT EXIST. APPLY DOMINANCE RULE FOR GAME THEORY TO REDUCE THE MATRIX INTO 2*2 MATRIX FORM

RULES OF DOMINANCE:

REMOVE COLUMN WHICH HAS VALUES MORE THAN (OR EQUAL)THE OTHER "COLUMN WHICH HAS LOWER VALUES"

REMOVE ROW WHICH HAS VALUES LOWER THAN (OR EQUAL) THE OTHER "ROW HAS HIGHER VALUES"

125 210 135 270

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