Why might an oligopoly be reluctant to change its price?
The major reason for this is that changing prices will typically do a firm in an oligopoly no good. If they lower their prices, their competitors will match what they do. If they raise their prices, their competitors will not. This means that neither move is likely to help.
If you lower your prices, you typically do so in hopes of getting more market share. However, if your competitors match (which they do in oligopoly because there are so few firms), you will not gain market share. Therefore, there is no point in lowering prices.
If you raise your prices (to try to make more profit), it is unlikely that your competitors will match. Because there are so few firms, each with large market share, your customers will likely go over to one of your competitors to get the lower price. You then lose market share.
So the small size and the interdependence of this market structure makes price changes relatively unwise.