Price rigidity refers to a situation in which whether there is change in demand and/or supply the price will be fixed, it will not change.

In an oligopolistic market firms are in a position to influence the prices.

However the firm's stick to their prices to avoid price war, but if a firm try to reduce the price the others will also react in the same manner so there will be no benefit.

In the same manner if a firm tries to raise the price, the other firms will not do so as a result of which, the firm which has intended to increase the price will lose its customers.

So oligopoly behaviour leads to price rigidity in an oligopolistic market.