Question

Bella Robinson and Steve Carson are running for a seat in the U.S. Senate. If both candidates campaign only in the major cities of the state, then Robinson is expected to get 80% of the votes; if both candidates campaign in only rural areas, then Robinson is expected get 75% of the votes; if Robinson campaigns exclusively in the city and Carson campaigns exclusively in the rural areas, then Robinson is expected to get 30% of the votes; finally, if Robinson campaigns exclusively in the rural areas and Carson campaigns exclusively in the city, then Robinson is expected to get 35% of the votes. (a) Construct the payoff matrix for the game. (Enter each percentage as a decimal.) Carson City Rural City Robinson Rural Is the game strictly determined? Yes ο No (b) Find the optimal strategy for both Robinson (row) and Carson (column).

Answer 1

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O.S5t soaleg i oPtimalmixcd So the Robimaon oi givem by b P: CP Co.uu o.5 P: uimg aa 0:80 be o:30, c:o-35 and da os od toR atd-b-c. 2U o-15-o-30 0.80+0-75-O.30-0-35 O.45 o-9 25-0-0-2. , 0.5 =1-P P.S : 1-0.5 0.5

oPtimal mixcd SO, the casom Szalegy by givem o.5 O.5