Cournot competition with incomplete information - game theory.Thank you! Consider the following version or the linear Cournot duopoly model. The market price, P is determined by(inverse) market demand:P = 1- Q if Q< 1, P = 0 otherwiseEach firm decides on the quantity to sell (market share): q1 and q2. Q = q1 + q2 total market demand.Both firms seek to maximize profits. There are no fixed costs. The marginal cost of producing each unit ofthe good: c1 and c2. c1 is common knowledge and equal to , however c2 is known only by firm 2. Firm1 believes that c2 is 'high" c = i with probability and 'low' c = 0 with probability . Firm l's beliefabout firm 2's cost is common knowledgeFind the pure strategy Bayes Nash Equilibrium and compare it to the situation in which the cost of firm2 is common knowledge. Does firm 2 have an incentive to reveal her cost when it is low? When it is high?What do you conclude?

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Answered: Consider the following version or the…

Microeconomic Theory

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ISBN:9781337517942

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Chapter15: Imperfect Competition

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Problem 15.3P

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Cournot competition with incomplete information - game theory.

Thank you!

Consider the following version or the linear Cournot duopoly model. The market price, P is determined by
(inverse) market demand:
P = 1- Q if Q< 1, P = 0 otherwise
Each firm decides on the quantity to sell (market share): q1 and q2. Q = q1 + q2 total market demand.
Both firms seek to maximize profits. There are no fixed costs. The marginal cost of producing each unit of
the good: c1 and c2. c1 is common knowledge and equal to , however c2 is known only by firm 2. Firm
1 believes that c2 is 'high" c = i with probability and 'low' c = 0 with probability . Firm l's belief
about firm 2's cost is common knowledge
Find the pure strategy Bayes Nash Equilibrium and compare it to the situation in which the cost of firm
2 is common knowledge. Does firm 2 have an incentive to reveal her cost when it is low? When it is high?
What do you conclude?

Definition Definition Economic decision-making framework that analyzes how different players optimize their outcomes with given pay-offs corresponding to their available strategies. The assumptions of game theory are: The number of players or competitors are finite/limited; All participants are rational The rules of the game are known to every player; and Each participant has a finite set of actions. A common way in which game theory is presented as an ( m x n ) matrix in which m represents the strategies of row player and n represents the strategies of column player. There are several limitations of game theory: Many businesses have a large number of competitors, and selecting an optimal strategy in these circumstances is difficult; Real-life business operating environments are full of uncertainty and difficult to model as a game theory; and The assumption of rationality and utility maximization isn't always an accurate portrayal of human nature.

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