The kinked demand curve model assumes that a business might face a dual demand curve for its product based on the likely reactions of other firms to a change in its price or another variable.
The assumption is that firms in an oligopoly are looking to protect and maintain their market share and that rival firms are unlikely to match another’s price increase but may match a price fall. I.e. rival firms within an oligopoly react asymmetrically to a change in the price of another firm.