Consider the price strategy of Delta Airlines for its Detroit-to-Philadelphia route. In this game spirit is a potential competitor along the same route. Spirit will make competitive profits on less-popular routes if it does enter the market for this service. The matrix representing this game is as follow:
Delta
Low Fare High Fare
Spirit Enter 0,0 5,10
Stay out 2,20 2,25
1.Is there a dominant strategy for either of the two companies? If so, what is the respective strategy?
2.Is there unique Nash equilibrium? If so what is it?
To determine the dominant strategies for the two companies, we need to compare the payoffs for each strategy in the matrix.
1. Delta Airlines:
- If Spirit enters the market and Delta sets a low fare, Delta's payoff is 0.
- If Spirit enters the market and Delta sets a high fare, Delta's payoff is 5.
- If Spirit stays out of the market and Delta sets a low fare, Delta's payoff is 2.
- If Spirit stays out of the market and Delta sets a high fare, Delta's payoff is 2.
2. Spirit Airlines:
- If Spirit enters the market and Delta sets a low fare, Spirit's payoff is 0.
- If Spirit enters the market and Delta sets a high fare, Spirit's payoff is 10.
- If Spirit stays out of the market and Delta sets a low fare, Spirit's payoff is 20.
- If Spirit stays out of the market and Delta sets a high fare, Spirit's payoff is 25.
From the above comparisons, we can see that there is no dominant strategy for Delta Airlines. The best strategy for Delta depends on Spirit's decision.
However, there is a dominant strategy for Spirit Airlines. Spirit's dominant strategy is to enter the market regardless of Delta's fare. This is because Spirit's payoff is higher when it enters the market, regardless of the fare Delta sets.
To find the Nash equilibrium, we look for the combination of strategies where neither company has an incentive to deviate from their chosen strategy. In other words, it is the point where both companies are making the best decisions given the other company's decision.
In this case, the unique Nash equilibrium is when Spirit enters the market and Delta sets a high fare, resulting in payoffs of 10 for Spirit and 5 for Delta. This is because Delta has a higher payoff by setting a high fare when Spirit enters, and Spirit has a higher payoff by entering the market regardless of Delta's fare.
So, the unique Nash equilibrium is (Spirit enters, Delta sets a high fare) with payoffs of (10, 5).