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.