Large language models demonstrate strong problem-solving abilities through reasoning techniques such as chain-of-thought prompting and reflection. However, it remains unclear whether these reasoning capabilities extend to a form of social intelligence: making effective decisions in cooperative contexts. We examine this question using economic games that simulate social dilemmas. First, we apply chain-of-thought and reflection prompting to GPT-4o in a Public Goods Game. We then evaluate multiple off-the-shelf models across six cooperation and punishment games, comparing those with and without explicit reasoning mechanisms. We find that reasoning models consistently reduce cooperation and norm enforcement, favoring individual rationality. In repeated interactions, groups with more reasoning agents exhibit lower collective gains. These behaviors mirror human patterns of "spontaneous giving and calculated greed." Our findings underscore the need for LLM architectures that incorporate social intelligence alongside reasoning, to help address—rather than reinforce—the challenges of collective action.