Why would a firm in balanced oligopoly choose a tit-for-tat strategy?

A firm appreciates that the most attractive outcome (charging low prices while the rival charges high prices, thereby capturing the entire market) is impossible because the rival will immediately react by lowering its own price. The best strategy is for both firms to charge high prices. But how can a firm achieve that outcome? By playing a tit-for-tat strategy, charging a high price and announcing that it will follow whatever price its rival chooses. In this way, the rival has no incentive to cut price.