We consider some variations of the edge-reinforced random walk. The focus will be on multiple (but finitely many) walkers which influence the edge weights together. Methods which have been used previously for studying reinforced walks break down and we therefore look at very basic models. First, we consider 2 walkers with linear reinforcement on a line graph comprising three nodes. We show that the edge weights evolve similarly to the setting with a single walker which corresponds to a Pólya urn.
We then look at an arbitrary number of walkers on Z with very general reinforcement. We show that in this case, the behaviour is also the same as for a single walker. If there is enough time, we will also have a look at unfinished work on reinforced walks with a bias and on evolving graphs.