  We consider goods that can be shared with k-hop neighbors (i.e., the set of
nodes within k hops from an owner) on a social network. We examine incentives
to buy such a good by devising game-theoretic models where each node decides
whether to buy the good or free ride. First, we find that social inefficiency,
specifically excessive purchase of the good, occurs in Nash equilibria. Second,
the social inefficiency decreases as k increases and thus a good can be shared
with more nodes. Third, and most importantly, the social inefficiency can also
be significantly reduced by charging free riders an access cost and paying it
to owners, leading to the conclusion that organizations and system designers
should impose such a cost. These findings are supported by our theoretical
analysis in terms of the price of anarchy and the price of stability; and by
simulations based on synthetic and real social networks.
