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In this question you are asked to compute the rationalizable strategies in linear Bertrand duopoly with...

In this question you are asked to compute the rationalizable strategies in linear Bertrand duopoly with “imperfect substitutes.” We have two firms N = {1, 2}, each with zero marginal cost. Simultaneously, each firm i sets a price pi ∈ P = [0, 10]. The demand for the good firm i sells, as a function of p1 and p2) is Qi (p1, p2)=1+ pj − pi. Each firm i maximizes its own profit πi (p1, p2) = piQ (p1,p2).

(a) Given any price pj set by the other firm, what is the best price pBR i for firm i? Plot a graph of best response curves.

(b) Compute the pure strategy Nash equilibrium.

(c) Compute all the rationalizable strategies.

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Expert Solution

Rahul Sunny answered 1 year ago
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