Two merchants are planning to build competing stores to serve an area of three s

Question

Two merchants are planning to build competing stores to serve an area of three small cities. The fraction of the total population that live in each city is shown in the table to the right. If both merchants locate in the same city, merchant A will get 65% of the total business. If the merchants locate in different cities, each will get 80% of the business in the city it is in, and A will get 60% of the business from the city not containing B. Payoffs are measured by the number of percentage points above or below 50%. Write a payoff matrix for this game. Is this game strictly determined? Write a payoff matrix for this game where the first entry in the first row of the payoff matrix represents both merchants A and B locating a store in city 1. (Type an integer or decimal for each matrix element.)

Explanation / Answer

Merchant B

City 1

City 2

City 3

Merchant A

City 1

15+10+10     -15

30+10+10      30

30+10+10      30

City 2

30+10+10      30

15+10+10     -15

30+10+10      30

City 3

30+10+10      30

30+10+10      30

15+10+10     -15

Merchant B

City 1

City 2

City 3

Merchant A

City 1

15+10+10     -15

30+10+10      30

30+10+10      30

City 2

30+10+10      30

15+10+10     -15

30+10+10      30

City 3

30+10+10      30

30+10+10      30

15+10+10     -15

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