The theory of the kinked demand curve is that

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The kinked demand curve theory suggests that a firm's competitors will follow it in a price decrease (to maintain market share and prevent losing customers), but not follow it in a price increase (to avoid losing market share and customers themselves). This creates a situation where the demand curve facing the firm is "kinked" at the current price level, with a relatively elastic demand curve for price decreases and a relatively inelastic demand curve for price increases. As a result, the firm is more likely to maintain the status quo price rather than risk losing market share and profits.

The Theory of the Kinked Demand Curve Is That