The classical Polya urn process is a reinforcement process, in which there are balls of different color in the urn, we take out a ball at random, and the color that was just out of it gets an advantage for all future turns: we return this ball to the urn and add another one of the same color.   

    However, in this process on every step all the colors are competing. What will happen if on different steps there will be different subsets of competing colors? For instance, if there are companies that compete on different markets, or if a signal is choosing its way to travel?   

    Some questions here have nice and simple answers; my talk will be devoted to the results of our joint project with Mark Holmes and Christian Hirsch on the topic.