Governments should intervene in such markets because of allocative and productive inefficiency.
An oligopoly market is one characterised by a small number of dominant large firms, each having high market share. They sell differentiated products and are price setters. Additionally, barriers to entry is high. Oligopolistic markets suffer from inefficiency and welfare loss arises because the firms fail to allocate resources efficiently (they are not allocating at the optimal output which maximizes producer/consumer welfare) and are also productive inefficient.
Particularly in a collusive oligopoly, intervention is required as the firms may be fixing prices and engage in unfair competition. In economics, welfare is maximized at socially optimal output at Q where DD=SS, or AR=MC. This is where the allocation is said to be pareto optimal- where nobody can be made better off without anyone made worse off. However, because O is a price setter, it is able to determine its own price at MC=MR(which is the profit max level of output), assuming that maximize profits. Therefore it earns more profit by producing less than the socially optimal output at Q1, it restricts output so that it can charge a higher price to max profit. It allocates at Q1 instead the socially optimal Q.
The firm is allocatively inefficient. Instead of producing at MC=AC, it produces to the left of AC. Also, the firm is productive inefficient because it fails to produce at the min AC; ie it is not maximizing the use of resources. It usually produces to the left of min AC, suggesting inability to maximize capacity. The firm is productively inefficient. Hence, there is under-allocation in this market, resulting in a loss of welfare represented by the red triangle (DWL). This is because in imperfect competition, the existence of barriers to entry prevents new competitors from entering, making existing firms complacent and having less incentive to produce at the minimum average cost.
However, the government does not have to intervene in all oligopolistic market. In markets that are non-collusive, there might be high degree of competition and firms have high incentive to compete using product differentiation and innovation. They will be dynamic efficient because they have incentive to do so (like automobile firms engage in new technology such as auto-driving cars or electric energy). Free market is efficient and such firms should be allowed to make excess profits which gives them ability to compete. On the other hand, the collusive oligopoly will be inefficient and hence requires intervention.
Government can intervene in dominant firms by privatizing or liberalizing the markets
This is where they sell state own enterprise like public transports/communication to private operators, who are profit driven and more efficient than state run entity, which tend to be productively inefficient. Government can open up the markets and allow for more competition and allowing firms to be more efficient and reduce complacency. Firms start to reduce cost to maximize profits, achieving lower levels of productively inefficiency. This also reduces market control and allocative inefficiency.