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. There are no dominated strategies here for either station as there is no case where each station can do the best no matter what the other station does.

b. There is one pure strategy Nash equilibrium to this game and this is given by (B,C) with payoffs of (1,2) respectively.

c. The Nash equilibrium would be (A,D) in this sequential game with payoffs of (2,5). This is an increase in payoffs over part b.

d. The Nash equilibrium would be (A,E) in this sequential game with payoffs of (5,3).This is an increase in payoffs over part b.

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