If we compare this experiment to the outlined examples we can draw some similarities. The people of Catalonia and the Democrats in the US also have strong cross-group competition. For Catalonia, this is the country Spain and for the Democrats, these are the Republicans. They also have their own identity (in the form of their own rituals, cultural values, flags/colors).
So is there a solution which can eliminate the created prejudice? The Robbers cave experiment provides us with a possible solution. How can we eliminate the artificially created prejudice among the two groups? In the third stage of the experiment, the researchers created situations in which the two groups had to work together in order to solve the problem. These teambuilding activities lead to a situation where the boys of the separated groups liked each other much more because of these team-building activities. Undoing the damage by collaboration and the creation of a common area. What brought the two groups together was a mythical third group, ‘the common enemy’ which spurred more 'us' vs 'them' with them being harmful outsiders that had been made up by the experimenters.
To bring big and small groups together it is thus important to create collaboration and a shared enemy. In the case of Spain and Catalonia, this could be in the form of a soccer World Cup for example. Football is both big in Catalonia and Spain and a good result for the national team with a mixture of players of Catalonia and Spain brings the two parties closer together. Similar the Democrats and Republicans learn to dislike each other but are also taught to hate a harmful third party, the terrorist, even more. The conclusion we can draw is thus that by adding collaboration and a common enemy we can bring groups closer together.