Finding Best Responses
A practical technique for identifying best responses in a payoff matrix is to systematically analyze each player's choices for every possible action by their opponent. The best response is the one yielding the highest payoff. For the game between Anil and Bala, this check reveals that Anil's best response is to grow cassava if Bala grows rice, and to grow rice if Bala grows cassava. A similar check for Bala shows that her best response is to always grow rice, regardless of Anil's choice. This systematic analysis, often visualized with dots or circles in the matrix, is performed for both players to find all best responses.
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Introduction to Microeconomics Course
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Ch.4 Strategic interactions and social dilemmas - The Economy 2.0 Microeconomics @ CORE Econ
The Economy 2.0 Microeconomics @ CORE Econ
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Determining Anil's Best Response if Bala Chooses Rice
Finding Best Responses
Dominant Strategy
Two competing firms, Firm A and Firm B, must simultaneously decide whether to 'Launch a new product' or 'Maintain the current product line'. The resulting profits for each firm depend on the actions of both, as shown in the following payoff structure, where the first number in the parentheses is Firm A's profit and the second is Firm B's profit:
- If both firms Launch: ($50 million, $50 million)
- If Firm A Launches and Firm B Maintains: ($120 million, $30 million)
- If Firm A Maintains and Firm B Launches: ($40 million, $100 million)
- If both firms Maintain: ($80 million, $80 million)
Given this information, if you know that Firm B has decided to 'Launch a new product', what is the best response for Firm A to maximize its own profit?
Two competing coffee shops, The Daily Grind and Brew & Co., are deciding on a daily promotion. The table below shows the daily profit (in dollars) for each shop based on the combination of strategies they choose. The first number in each pair is The Daily Grind's profit, and the second is Brew & Co.'s profit.
Payoff Matrix:
Brew & Co: Latte Discount Brew & Co: Muffin Combo Brew & Co: No Special Grind: Latte Discount ($100, $100) ($150, $80) ($160, $90) Grind: Muffin Combo ($110, $140) ($120, $120) ($200, $50) Grind: No Special ($80, $220) ($180, $180) ($140, $140) Match each of Brew & Co.'s potential strategies to The Daily Grind's best response to maximize its own profit.
Roommate Chore Dilemma
Farmer's Irrigation Choice
Two roommates, Alex and Ben, must decide independently whether to 'Clean' their shared apartment or 'Relax'. The satisfaction they each get from their decision depends on what the other person does, as shown in the payoff table below. The first number in each cell is Alex's satisfaction score, and the second is Ben's.
Ben: Clean Ben: Relax Alex: Clean (8, 8) (3, 10) Alex: Relax (10, 3) (0, 0) Statement: If Ben decides to 'Clean', Alex's best response is also to 'Clean'.
Determining a Best Response
Analyzing Strategic Choices in a Market Entry Game
Consider the payoff matrix below, which shows the profits (in thousands of dollars) for two competing firms based on their advertising budget decisions. The first number in each cell is the profit for Innovate Corp, and the second is for Tech Solutions.
Tech Solutions: Increase Tech Solutions: Maintain Innovate Corp: Increase (60, 50) (____, 30) Innovate Corp: Maintain (40, 70) (80, 80) If Tech Solutions chooses to 'Maintain' its budget, what is the minimum whole number profit (in thousands of dollars) that must go in the blank to make 'Increase' the best response for Innovate Corp?
A manager at 'Pizza Palace' is trying to decide on a pricing strategy. Their profit depends on the choice made by a competing business, 'Burger Barn'. The manager wants to determine their single most profitable action, assuming they know that Burger Barn has committed to a specific strategy. Arrange the following steps into the logical order the manager should follow to identify their 'best response'.
Evaluating a Strategic Recommendation
Payoff Determination in the Anil and Bala Game
Determining Anil's Best Response if Bala Chooses Rice
Determining Anil's Best Response if Bala Chooses Cassava
Finding Best Responses
Learn After
Determining Anil's Best Response if Bala Chooses Rice
Determining Anil's Best Response if Bala Chooses Cassava
Finding a Column Player's Best Responses
Nash Equilibrium
Bala's Dominant Strategy to Grow Rice
Rice-Cassava Game as a Dominant Strategy Equilibrium
Determining Anil's Best Response if Bala Chooses Cassava in the Specialization Game
Anil's Best Response to Rice in the Specialization Game
Strategic Business Decision
Consider the following payoff matrix for a game between two firms, Firm 1 and Firm 2. The payoffs are listed as (Firm 1's profit, Firm 2's profit).
Firm 2: Advertise Firm 2: Don't Advertise Firm 1: Advertise (10, 5) (15, 0) Firm 1: Don't Advertise (6, 8) (12, 2) Based on this matrix, what is the complete set of Firm 1's best responses?
Consider the following payoff matrix for a game between two companies, where payoffs represent profits in thousands of dollars and are listed as (Company 1's profit, Company 2's profit).
Company 2: High Price Company 2: Low Price Company 1: High Price (100, 100) (20, 120) Company 1: Low Price (120, 30) (50, 50) Statement: If Company 1 anticipates that Company 2 will set a 'Low Price', Company 1's best response is to also set a 'Low Price'.
Identifying Best Responses in a Game
Consider the following payoff matrix for a game between two players. The payoffs are listed as (Player A's payoff, Player B's payoff). Match each scenario with the corresponding player's best response.
Player B: Left Player B: Right Player A: Up (3, 5) (1, 6) Player A: Down (4, 2) (2, 1) To systematically identify a player's best responses in a game presented in a payoff matrix, a specific sequence of steps should be followed. Arrange the following steps into the correct logical order for this process.
Consider the following payoff matrix for a game between two companies, InnovateCorp and TechGiant. The payoffs represent profits in millions of dollars and are listed as (InnovateCorp's profit, TechGiant's profit).
TechGiant: Launch TechGiant: Wait InnovateCorp: Launch (10, 8) (20, 2) InnovateCorp: Wait (5, 15) (X, 4) Currently, if TechGiant chooses to 'Wait', InnovateCorp's best response is to 'Launch'. For 'Wait' to become InnovateCorp's best response to TechGiant choosing 'Wait', what must be true about the value of X?
Comparative Analysis of Strategic Scenarios
Consider the following payoff matrix for a game between two players, Alex and Ben. The payoffs are listed as (Alex's payoff, Ben's payoff).
Ben: Strategy Y Ben: Strategy Z Alex: Strategy A (5, 2) (1, 8) Alex: Strategy B (3, 6) (10, 4) If Alex assumes that Ben will choose 'Strategy Y', which of the following statements correctly identifies Alex's best response and the reason for it?
Consider the following payoff matrix for a game between two companies, A-Corp and B-Corp. The payoffs, representing profits, are listed as (A-Corp's profit, B-Corp's profit).
B-Corp: High Price B-Corp: Low Price A-Corp: High Price (50, 50) (20, 60) A-Corp: Low Price (__, 20) (30, 30) For 'Low Price' to be A-Corp's best response when B-Corp chooses 'High Price', the missing payoff for A-Corp must be a number greater than ____.
The Dot-and-Circle Method for Finding Best Responses