**Understanding Duopoly Through a Payoff Matrix:**The table presented is a payoff matrix for two firms, Sealy and Tempurpedic, engaged in a single-stage duopoly game. Each firm independently decides whether to produce 3,000 or 4,000 mattresses, without knowing the other firm's decision. Their respective economic profits depend on both firms' choices.**Payoff Matrix Explanation:**- **Sealy's Choices:** - Producing 3,000 mattresses - Producing 4,000 mattresses- **Tempurpedic's Choices:** - Producing 3,000 mattresses - Producing 4,000 mattresses**Outcomes:**1. **Both Produce 3,000 Mattresses:** - Sealy: $25,000 - Tempurpedic: $25,0002. **Sealy Produces 3,000 and Tempurpedic Produces 4,000:** - Sealy: $10,000 - Tempurpedic: $35,0003. **Sealy Produces 4,000 and Tempurpedic Produces 3,000:** - Sealy: $35,000 - Tempurpedic: $10,0004. **Both Produce 4,000 Mattresses:** - Sealy: X - Tempurpedic: XThe game's structure hints at a potential prisoner’s dilemma, a situation in economic theory where two parties, unable to communicate, might not cooperate even if it's in their best interest. The specific range for "X" that would create this dilemma is among the choices presented below the table:a. $10,000 and $25,000 b. $25,000 and $35,000 c. $10,000 and $35,000 d. $35,000 and $70,000 e. $45,000 and $70,000 This scenario challenges students to explore how firms may struggle with cooperation and competition in economic modeling, identifying conditions for the prisoner’s dilemma.

Prisoners dilemma is an important element of game theory that shows paradox where agents in game attempting to enhance their individual pay off take the decision which is different than the optimal decision. If we want to compare the given payoff matrix with the prisoners dilemma then we must relate the behaviour of these firms with the prisoners in the prisoners dilemma.Confess-confess strategy gives both prisoners 5 years of punishment. Here in the same cell we see both firms cooperating and gaining 3000,3000 Confess- don’t confess outcome (-1,-10) gives greater advantage to the prisoner who cheats/ does not cooperate. (Prisoner A) Here the firm which does not cooperate and produce more than other gets the greater advantage.(tempurpedic) Don’t confess-confess outcome (-10,-1) gives greater advantage to the prisoner who cheats/ does not cooperate. (Prisoner B) Here the firm which does not cooperate and produce more than other gets the greater advantage.(sealy) Don’t confess-Don’t confess is the strategy we need to watch where the pay-off are more than -1 but and -5. If we relate that to our payoff matrix then we can conclude the X should be between 1000and 25

Business

Economics

The following table shows two firms in a single-stage duopoly game. Each firm makes its decision without knowledge of the other firm's decision. The payoffs for each firm represent economic profits, and each firm strictly prefers more economic profit than less. This game would be considered a prisoner's dilemma if X is between Tempurpedic Produce 3,000 mattresses $25,000 Produce 4,000 mattresses $35,000 Produce 3,000 $10,000 $25,000 mattresses Sealy $10,000 X Produce $35,000 4,000 mattresses d. $35,000 and $70,000. e. $45,000 and $70,000. a. $10,000 and $25,000. b. $25,000 and $35,000. $10,000 and $35,000. с.

The following table shows two firms in a single-stage duopoly game. Each firm makes its decision without knowledge of the other firm's decision. The payoffs for each firm represent economic profits, and each firm strictly prefers more economic profit than less. This game would be considered a prisoner's dilemma if X is between Tempurpedic Produce 3,000 mattresses $25,000 Produce 4,000 mattresses $35,000 Produce 3,000 $10,000 $25,000 mattresses Sealy $10,000 X Produce $35,000 4,000 mattresses d. $35,000 and $70,000. e. $45,000 and $70,000. a. $10,000 and $25,000. b. $25,000 and $35,000. $10,000 and $35,000. с.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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