There are two main theories that explain and could help to reduce prejudice, one of them is the realistic conflict theory which states that social categorisation and direct competition over scarce resources is needed and the social identity theory states that prejudice comes from social categorisation which is done to boost ones own self esteem, and no realistic conflict is needed.
There are also some experiments testing each theory; one of the experiments testing the remote conflict theory is the experiment done by Sherif et al (1961) where the experimenters got a summer camp of boys and split them into two groups (social categorisation) and the boys also gave their teams their own name and flag. They were pitted against each other e.g. tug of war, and lots of other games competing for four knife blades and a medal, and prejudice increased quite a lot and fights were happening so they set them unexpected tasks, working toward one goal e.g. the camp truck breaking down and them having to pull it back, and this reduced prejudice. Brown supported this by looking at the earthquake in central India which killed over 30000 people and Muslims and Hindus were helping each other. .
So this in a way explains prejudice in that it gives you two groups, (in real life it could be the Americans prejudice towards the Chinese in the 19th c) and it gives you the scarce resources that could start of prejudice (again in the 19th c the Americans didn't like the Chinese because they were taking all the jobs) therefore it explains how prejudice can arise. .
So according to this experiment if society was desegregated and had only superordinate goals then there would be no prejudice but the experiment lacks ecological validity and could in fact increase prejudice in the real world, as tested by Stephen (1978).