Nash Equilibrium

Two competing firms, Firm A and Firm B, must each decide whether to set a 'High Price' or a 'Low Price' for their product. Their profits depend on the choices both firms make. The potential outcomes are listed below, with Firm A's profit always listed first and Firm B's second.

• If both choose 'High Price', the profits are (A: $50, B: $50).
• If Firm A chooses 'High Price' and Firm B chooses 'Low Price', the profits are (A: $20, B: $70).
• If Firm A chooses 'Low Price' and Firm B chooses 'High Price', the profits are (A: $70, B: $20).
• If both choose 'Low Price', the profits are (A: $30, B: $30).

Assuming Firm B has already decided to set a 'High Price', what should Firm A do to achieve the best possible outcome for itself?

Strategic Location Choice

Coffee Shop Competition Strategy

Two construction companies, BuildIt and ConstructCo, are bidding on a project. They can each submit a 'Low Bid' or a 'High Bid'. The matrix below shows the potential profit for each company based on their combined choices. Profits are listed as (BuildIt's Profit, ConstructCo's Profit).

Match each of ConstructCo's potential actions to BuildIt's best response (the bidding strategy that maximizes BuildIt's own profit).

Two competing local businesses, 'The Corner Store' and 'Main Street Market', are deciding whether to run a 'Weekday Special' or a 'Weekend Sale'. Their potential daily profits are dependent on the choices made by both stores. The profits are listed as (Corner Store's Profit, Main Street Market's Profit).

• If both choose 'Weekday Special': ($1,000, $900)
• If both choose 'Weekend Sale': ($1,800, $1,700)
• If Corner Store chooses 'Weekday Special' and Main Street Market chooses 'Weekend Sale': ($800, $2,000)
• If Corner Store chooses 'Weekend Sale' and Main Street Market chooses 'Weekday Special': ($2,200, $700)

Statement: Assuming Main Street Market has decided to run a 'Weekday Special', The Corner Store's best response to maximize its own profit is to also run a 'Weekday Special'.

Two rival companies, SwiftLogistics and ApexMovers, are deciding whether to invest in 'Drone Delivery' or 'Electric Trucks'. Their potential profits (in millions of dollars) are dependent on the choices made by both, and are listed as (SwiftLogistics' Profit, ApexMovers' Profit).

• If both choose 'Drone Delivery': ($5, $5)
• If both choose 'Electric Trucks': ($8, $10)
• If SwiftLogistics chooses 'Drone Delivery' and ApexMovers chooses 'Electric Trucks': ($2, $12)
• If SwiftLogistics chooses 'Electric Trucks' and ApexMovers chooses 'Drone Delivery': ($15, $3)

If ApexMovers decides to invest in 'Electric Trucks', the highest possible profit SwiftLogistics can achieve is $______ million.

Evaluating a Strategic Business Claim

Innovate Inc. and Tech Giant Corp. are two software companies deciding whether to develop for 'OS-Alpha' or 'OS-Beta'. The table below shows the potential profits for each company (in millions of dollars) based on their choices, with Innovate Inc.'s profit listed first and Tech Giant Corp.'s second.

Tech Giant Corp. has announced they will develop for 'OS-Alpha'. Arrange the following steps in the correct logical order for Innovate Inc. to decide which action will maximize its own profit.

Food Truck Location Strategy

Two students, Liam and Maria, are working on a project. Their grade depends on the effort each puts in. They can either 'Work Hard' or 'Slack Off'. The possible outcomes, represented as (Liam's Grade, Maria's Grade), are:

• If both 'Work Hard': (9, 9)
• If Liam 'Works Hard' and Maria 'Slacks Off': (6, 8)
• If Liam 'Slacks Off' and Maria 'Works Hard': (8, 6)
• If both 'Slack Off': (5, 5)

If Maria has already decided she will 'Work Hard', which action should Liam take to maximize his own grade?