  Recently, Apt and Markakis introduced 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 (products). To analyze
these networks we introduce social network games in which product adoption is
obligatory.
  We show that when the underlying graph is a simple cycle, there is a
polynomial time algorithm allowing us to determine whether the game has a Nash
equilibrium. In contrast, in the arbitrary case this problem is NP-complete. We
also show that the problem of determining whether the game is weakly acyclic is
co-NP hard.
  Using these games we analyze various types of paradoxes that can arise in the
considered networks. One of them corresponds to the well-known Braess paradox
in congestion games. In particular, we show that social networks exist with the
property that by adding an additional product to a specific node, the choices
of the nodes will unavoidably evolve in such a way that everybody is strictly
worse off.
