  Recently, we introduced in arXiv:1105.2434 a model for product adoption in
social networks with multiple products, where the agents, influenced by their
neighbours, can adopt one out of several alternatives. We identify and analyze
here four types of paradoxes that can arise in these networks. To this end, we
use social network games that we recently introduced in arxiv:1202.2209. These
paradoxes shed light on possible inefficiencies arising when one modifies the
sets of products available to the agents forming a social network. One of the
paradoxes corresponds to the well-known Braess paradox in congestion games and
shows that by adding more choices to a node, the network may end up in a
situation that is worse for everybody. We exhibit a dual version of this, where
removing available choices from someone can eventually make everybody better
off. The other paradoxes that we identify show that by adding or removing a
product from the choice set of some node may lead to permanent instability.
Finally, we also identify conditions under which some of these paradoxes cannot
arise.
