  Game-theoretic analyses of distributed and peer-to-peer systems typically use
the Nash equilibrium solution concept, but this explicitly excludes the
possibility of strategic behavior involving more than one agent. We examine the
effects of two types of strategic behavior involving more than one agent,
sybils and collusion, in the context of scrip systems where agents provide each
other with service in exchange for scrip. Sybils make an agent more likely to
be chosen to provide service, which generally makes it harder for agents
without sybils to earn money and decreases social welfare. Surprisingly, in
certain circumstances it is possible for sybils to make all agents better off.
While collusion is generally bad, in the context of scrip systems it actually
tends to make all agents better off, not merely those who collude. These
results also provide insight into the effects of allowing agents to advertise
and loan money. While many extensions of Nash equilibrium have been proposed
that address collusion and other issues relevant to distributed and
peer-to-peer systems, our results show that none of them adequately address the
issues raised by sybils and collusion in scrip systems.
