  Participatory crowd sensing social systems rely on the participation of large
number of individuals. Since humans are strategic by nature, effective
incentive mechanisms are needed to encourage participation. A popular mechanism
to recruit individuals is through referrals and passive incentives such as
geometric incentive mechanisms used by the winning team in the 2009 DARPA
Network Challenge and in multi level marketing schemes. The effect of such
recruitment schemes on the effort put in by recruited strategic individuals is
not clear. This paper attempts to fill this gap. Given a referral tree and the
direct and passive reward mechanism, we formulate a network game where agents
compete for finishing crowd sensing tasks. We characterize the Nash equilibrium
efforts put in by the agents and derive closed form expressions for the same.
We discover free riding behavior among nodes who obtain large passive rewards.
This work has implications on designing effective recruitment mechanisms for
crowd sourced tasks. For example, usage of geometric incentive mechanisms to
recruit large number of individuals may not result in proportionate effort
because of free riding.
