Joe is the owner of the PetroCanada Mini Mart,Sam is the owner of the BP Mini Mart,and together they are the only gas stations in town.At the current price of $1 per litre,each receives total revenue of $1000.Joe is considering cutting his price to 90 cents per litre,which would increase his total revenue to $1350.If Sam's price remains at $1 per litre after Joe cuts his price,Sam will collect $500 in revenue.If Sam cuts his price to 90 cents per litre,his total revenue would also rise to $1350 if Joe continues to charge $1 per litre.Joe will collect $500 in revenue if he keeps his price at $1 per litre while Sam lowers his to 90 cents per litre.Joe and Sam will receive $900 each in total revenue if they both lower their price to 90 cents per litre.You may find it easier to answer the following questions if you fill in the payoff matrix below.
-Which of the following is NOT true of a Nash equilibrium in a game involving players A and B?
A) Given the strategies of B,player A has chosen the highest payoff strategy.
B) Neither player A nor player B wants to choose a different strategy.
C) Both players would not wish to change their choices.
D) Both players must have dominant strategies.
E) Given the strategies of A,player B has chosen the highest payoff strategy.

Question

Joe is the owner of the PetroCanada Mini Mart,Sam is the owner of the BP Mini Mart,and together they are the only gas stations in town.At the current price of $1 per litre,each receives total revenue of $1000.Joe is considering cutting his price to 90 cents per litre,which would increase his total revenue to $1350.If Sam's price remains at $1 per litre after Joe cuts his price,Sam will collect $500 in revenue.If Sam cuts his price to 90 cents per litre,his total revenue would also rise to $1350 if Joe continues to charge $1 per litre.Joe will collect $500 in revenue if he keeps his price at $1 per litre while Sam lowers his to 90 cents per litre.Joe and Sam will receive $900 each in total revenue if they both lower their price to 90 cents per litre.You may find it easier to answer the following questions if you fill in the payoff matrix below. 
-Which of the following is NOT true of a Nash equilibrium in a game involving players A and B?
A) Given the strategies of B,player A has chosen the highest payoff strategy. 
B) Neither player A nor player B wants to choose a different strategy. 
C) Both players would not wish to change their choices. 
D) Both players must have dominant strategies. 
E) Given the strategies of A,player B has chosen the highest payoff strategy.

Quizplus · Accepted Answer

The question mentions nothing about dominant strategies, so it cannot be assumed that both players must have one. A Nash equilibrium occurs when both players choose their best strategy given the other player's choice, and none have an incentive to change their strategy unilaterally. From the payoff matrix, it can be seen that the Nash equilibrium occurs when both players lower their price to 90 cents per litre. At this point, neither player has an incentive to change their strategy unilaterally, as doing so would result in a lower payoff.

Joe Is the Owner of the PetroCanada Mini Mart,Sam Is