4. Two gas stations are competing on one corner. Each firm is trying to pick a s

Question

4. Two gas stations are competing on one corner. Each firm is trying to pick a strategy. The market conditions are such that they face the following payo Station 2 A 0 4 2 5 B 12 3 1 4 0 (a) Does either stations have any dominant or domi- nated strategies? (b) If the stations choose their actions simultaneously, what are the possible Nash equilibria, and what would be the payoffs? (c) If station 1 moves first, what is the Nash equilib- rium? Did they increase their payoff over part (b)? (d) If station 2 moves first, what is the Nash equilib- rium? Did they increase their payoff over part (b)?

Explanation / Answer

A) When 2 choses C, 1 chooses B

When 2 chooses D, 1 chooses B

When 2 chooses E, 1 chooses A

So, 1 has dominant strategy to chose B

Similarly,

When 1 chooses A, 2 chooses D

When 1 chooses B, 2 chooses C

So, 2 has no dominant strategy

B) Nash: (B,C) giving payoff (1,2)

C) If 1 moves first, it will chose B and then 2 will choose C

So, nash will be (B,C)

D) If 2 moves first, it will chose D and then 1 will choose B

So, Nash will be (B,D)

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