Question

Suppose you are given the following one-shot, simultaneous-move game:                                     

BP and Exxon are deciding whether or not to charge a high price or a low price for       gasoline sales tomorrow. The two firms cannot collude, and both will post their prices tomorrow at the same time. This game has the following payoff matrix (profits for the day are in parentheses):

           

                                                                        Exxon

	High Price	Low Price
High Price	($800, $800)	(-$300, $1,200)
Low Price	($1,200, -$300)	($500, $500)

BP   

            What would be the solution to this game? Explain your reasoning.

Answer 1

To find the solution to this game, we will make four cases:

First Case: Let's assume BP decides to charge the high price, then Exxon will charge Low price because of higher payoff i.e. $1200>$800.

Second Case: Let's assume BP decides to charge the low price, then Exxon will charge Low price again because of higher payoff i.e. -$300 < $500.

So, from the above two cases, we can conclude that Exxon will charge "Low price" irrespective of the choice made by BP.

Third Case: Let's assume this time Exxon will charge High Price, then BP will charge Low price because of higher payoff i.e. $1,200> $800.

Fourth Case: Let's assume this time Exxon will charge Low Price, then BP will charge Low price again because of higher payoff i.e. $500> - $300.

So, from the above two cases, we can conclude that BP will charge "Low price" irrespective of the choice made by Exxon.

From the above four cases, we can conclude that both BP and Exxon will charge Low price irrespective of what other firm is charging and they do not have any incentive to deviate from this strategy. Hence, the solution to this game is " Low Price, Low Price" i.e ($500,$500).