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:
To analyze this game, we can use the concept of game theory, which helps us understand how players make decisions in strategic situations.
The matrix you provided represents a simultaneous game, where each player (Delta Airlines and Spirit) chooses a strategy without knowing the other player's strategy. The payoffs in the matrix represent the profits each player would earn based on their strategy choices.
Let's break down the given matrix:
Delta Airlines
| Enter Market | Stay Out |
_______________________________________________
| Enter Market | $5 million | $4 million |
|________________|________________|____________|
| Stay Out | $3 million | $1 million |
|________________|________________|____________|
In this game, Delta Airlines and Spirit have two possible strategies: "Enter Market" or "Stay Out." The rows of the matrix represent Delta Airlines' strategies, while the columns represent Spirit's strategies.
The payoff numbers represent the expected profits (in millions of dollars) for Delta Airlines and Spirit based on their chosen strategies.
For example, if Delta Airlines chooses to "Enter Market" and Spirit also chooses to "Enter Market," Delta Airlines would earn $5 million and Spirit would earn $4 million. Likewise, if Delta Airlines chooses to "Stay Out" and Spirit chooses to "Stay Out," Delta Airlines would earn $1 million and Spirit would earn $3 million.
To analyze such a game, we look for any dominant strategies or Nash equilibria. A dominant strategy occurs when a player's chosen strategy is the best regardless of the other player's strategy. A Nash equilibrium is a situation where both players are making optimal decisions, given the other player's strategy.
By examining the given matrix, we can identify that there is no dominant strategy for either player. Delta Airlines could potentially earn $5 million if it chooses to enter the market, but it could also earn $4 million if it stays out. Similarly, Spirit could potentially earn $3 million if it stays out, but it could also earn $4 million if it enters the market.
To find the Nash equilibrium, we need to consider the strategies that are optimal for both players, assuming their choices are known to each other. In this case, the Nash equilibrium occurs when both players choose to "Enter Market." This is because both Delta Airlines and Spirit would earn more profits compared to the other possible combination of strategies.
However, it's important to note that this analysis is based solely on the given matrix and doesn't consider other factors such as market demand, pricing strategies, or other competitive dynamics. Real-life situations can be more complex, and additional considerations might influence the players' decisions and outcomes.