Yes, but this is not the competition of the brute animal world, the competition of force. Instead, capitalism thrives because people compete to cooperate with one another. A market is simply a social arrangement in which people are free to cooperate with whomever they please. Socialism, on the other hand, rewards mutually destructive behavior and punishes cooperation and productivity. In socialism, the late mergers rise to the top.
Socialism is the institutionalization of the free rider problem.
In socialism, different interest groups fight to grab the levers of power. These groups lobby the government for subsidies and favoritism at the expense of the rest of society. In socialism, those most adept at using the brute force of the state rise to power over the rest of us. However, socialism is not otherwise a benevolent system. As Ludwig von Mises and his student Friedrick Hayek have shown, even socialists motivated to help people cannot in fact do so, because in their fatal conceit they try to run the lives of others without the requisite knowledge to do so effectively.