In the little town of Gas Pump, South Dakota, there are two gas stations across the street from each other, the East station and the West station.A local ordinance requires that they are permitted to change the price of gasoline only once a week at precisely 8:00a.m.on Monday and in 5 cent increments.For some time, the price of gasoline has been stable at $1.50 per gallon, but midweek, the price each station pays for gasoline changed to $1.49.Given the payoff matrix below, which of the following strategies is a pure strategy Nash equilibrium?

A) (hold, hold) and (raise, raise)
B) (cut, cut) and (hold, hold)
C) (cut, cut) , (hold, hold) , and (raise, raise)
D) (raise, raise)
E) No pure strategy Nash equilibrium exists.

Question

In the little town of Gas Pump, South Dakota, there are two gas stations across the street from each other, the East station and the West station.A local ordinance requires that they are permitted to change the price of gasoline only once a week at precisely 8:00a.m.on Monday and in 5 cent increments.For some time, the price of gasoline has been stable at $1.50 per gallon, but midweek, the price each station pays for gasoline changed to $1.49.Given the payoff matrix below, which of the following strategies is a pure strategy Nash equilibrium?

A) (hold, hold) and (raise, raise)
B) (cut, cut) and (hold, hold)
C) (cut, cut) , (hold, hold) , and (raise, raise)
D) (raise, raise)
E) No pure strategy Nash equilibrium exists.

Derek Warnstedt · Accepted Answer

Final Answer : A, Explanation :  A pure strategy Nash equilibrium occurs when both players are playing their best response to each other's strategy. In this case, if one station raises their price while the other holds, they will attract fewer customers and ultimately lose profits. If both stations cut their price, they will both lose profits. Therefore, the only pure strategy Nash equilibrium is for both stations to hold their price at $1.50 per gallon. Any other strategy would result in a less profitable outcome for both stations. (Note that choice C includes holding prices at $1.50 per gallon as a potential strategy, but also includes other strategies that would not be optimal in this situation.)

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