Recent work using decontextualized economic games suggests that cooperation is a dynamic decision-making process: Automatic responses typically support cooperation on average, while deliberation leads to increased selfishness. Here, we performed two studies examining how these temporal effects generalize to games with richer social context cues. Study 1 found that time pressure increased cooperation to a similar extent in games played with in-group members and out-group members. Study 2 found that time pressure increased cooperation to a similar extent in games described as competitions and games described as collaborations. These results show that previous positive effects of time pressure on cooperation are not unique to neutrally framed games devoid of social context and are not driven by implicit assumptions of shared group membership or cooperative norms. In doing so, our findings provide further insight into the cognitive underpinnings of cooperative decision making