Oligopoly and demand curve

Question:

Suppose the jeans industry is an oligopoly in which each firm sells its own distinctive brand of jeans, and each firm believes its rivals will not follow its price increases but will follow its price cuts. 

Draw and explain the demand curve facing each firm, and given this demand curve, does this mean that firms in the jeans industry do or do not compete against one another?

Summary:

This question discusses kinked demand curve, a dilemma in most microeconomic scenarios where two or more competing firms wage price wars and arrive at a price which seems to be kinked when plotted on a graph.