The study looked at how people's beliefs and preferences affect their decisions in social dilemmas. They found that when people play both roles in a game, their decisions are influenced by what they believe the other person will do. This can lead to a pattern where first and second moves are related. The researchers discovered that this connection is mainly due to second movers influencing beliefs, which then affect first movers' decisions. People tend to base their actions on what they think the other person will do. However, there is also a direct link between preferences and decisions, as knowing the true probability of the other person's cooperation still impacts one's own choices.