Gas Station Dilemma: Finding the Optimal Price

What is the dilemma faced by Joe and Sam, the owners of the only two gas stations in town?

If both players choose their dominated strategy, what will be their profit? And if both players choose their dominant strategy, what will be their profit?

1. $900; $1,000
2. $500; $1,350
3. $900; $1,350
4. $1,000; $900

Answer:

1. $900; $1,000

Joe and Sam, the owners of the only two gas stations in town, are facing a dilemma regarding the pricing of their gas. The data reveals that currently, both are charging $3 per gallon and earning a profit of $1,000 each. However, if Joe cuts his price to $2.90 while Sam continues to charge $3, their profits shift to $1,350 for Joe and $500 for Sam. On the other hand, if Sam cuts his price to $2.90 while Joe maintains his price at $3, the profits reverse, with Sam earning $1,350 and Joe earning $500.

The key lies in understanding dominated and dominant strategies. A dominated strategy is one that a player can choose to adopt in the future, while a dominant strategy is the plan they are currently working with. In this scenario, if both Joe and Sam choose their dominated strategy of cutting the price to $2.90, they will each earn a profit of $900. However, if both players stick to their dominant strategy of charging $3, they will each earn $1,000.

Therefore, the optimal strategy for Joe and Sam in maximizing their profits seems to be choosing their dominant strategy of maintaining the price at $3 per gallon.