The paper studies the competition between two oligopolies in their two-staged pricing. It proves that the price and the gross profit are negatively related to the switching cost, and that the higher the degree of relativity of the switching cost to the market share is, the lower the prices at the first pricing stage would be. The oligopoly that practices the lower price strategy at the first pricing stage would lose part of its share in the market at the second one. By comparing the switching cost to the cost on advertisement or promotion for new products, the paper discusses on the competition among neighboring oligopolies and points out that the profit of the oligopoly mainly comes from the switching cost.