Question

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).

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.

Answer 1