Derive the pure strategy nash equilibrium, Basic Statistics

There are two firms competing in quantity. Firm 1 and 2 set their quantities supplied, q1 and q2, respectively. The production costs are zero. The market price is given by

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where a ∈ (0,1/2) and b ≥0. Note that the inverse demand function is kinked at the point (1 - a, a).

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This is a simple one-shot game. The firms simultaneously set their quantities. The objective of each firm is to maximize its profit, that is,

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1. Derive the pure strategy Nash equilibrium and the equilibrium profits when b = 0.

Ans. 0.5 each

2. Derive the pure strategy Nash equilibrium and the equilibrium profits when b > 0. Note that two pure strategy Nash equilibria may exist.

Ans. All or nothing

3. Dose an increase in b benefit the two firms? This means that you should explain whether or not at increase in the demand size benefits the firm.

Posted Date: 3/20/2013 3:24:33 AM | Location : United States

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