In context of oligopoly, the kinky demand curve (kinked demand curve) hypothesis is designed to explain:

Kinked demand curve model is an initial attempt to explain sticky prices. In oligopolistic market if one firm increases its price then the other firms will not follow it. But if the firm decreases its price then other firms also decrease their prices otherwise they will lose the considerable part of their consumers. Firms do not want to raise their prices b/c even a small price increase will lose many customers. Firms also do not want to decrease the price b/c when one firm did so then price war will start from other firms. The kinked demand curve theory suggests that there will be price stickiness (price rigidity) in oligopolistic market and the firms will rely more on non-price competition to boost sales, revenue and profits. Some economists also say that this kinked demand model is also apply in monopolistic competition.}