Paradoxes in social networks with multiple products

We show that various paradoxes can arise in a natural class of social networks. They demonstrate that more services or products may have adverse consequences for all members of the network and conversely that restricting the number of choices may be beneficial for every member of the network. These phenomena have been confirmed by a number of empirical studies. In our analysis we use a simple threshold model of social networks introduced in Apt and Markakis (2011), and more fully in Apt and Markakis (2014). In this model 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. These paradoxes shed light on possible inefficiencies arising when one modifies the sets of products available to the agents forming a social network or the network structure. 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, according to which removing a product available to an agent 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 an agent may lead to permanent instability. Finally, we also identify conditions under which some of these paradoxes cannot arise.

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