If the firm were to reduce its price rivals would follow suit in order to protect its market share. Thus a reduction in price to P1 would bring about only a small increase in quantity demanded. Thus the firm would expect its demand curve to be relatively inelastic for reduction in price. Overall the firm will believe its demand curve to be kinked at the current price. Price cutting as a strategy tends to lead to a competitive downward spiral in firms prices and price wars which in turn leads of a fall in revenue.
Oligopolistic firms tend to prefer to engage in non-price competition.
The theory does not explain how oligopolists se the initial price, only why the price might be stable. The stickiness of price may have little to do with rival firms reaction patterns but with the administrative expense of changing price. If oligopolists act together collusively and jointly maximize profits then the same disadvantages as those experienced under a monopoly will be experienced. Depending on the size of the oligopoly there may be less scope for economies of scale to mitigate the effects of market power. Oligopolists are likely to engage in much more extensive advertising which increases the demand of the product.