  An exciting application of crowdsourcing is to use social networks in complex
task execution. In this paper, we address the problem of a planner who needs to
incentivize agents within a network in order to seek their help in executing an
{\em atomic task} as well as in recruiting other agents to execute the task. We
study this mechanism design problem under two natural resource optimization
settings: (1) cost critical tasks, where the planner's goal is to minimize the
total cost, and (2) time critical tasks, where the goal is to minimize the
total time elapsed before the task is executed. We identify a set of desirable
properties that should ideally be satisfied by a crowdsourcing mechanism. In
particular, {\em sybil-proofness} and {\em collapse-proofness} are two
complementary properties in our desiderata. We prove that no mechanism can
satisfy all the desirable properties simultaneously. This leads us naturally to
explore approximate versions of the critical properties. We focus our attention
on approximate sybil-proofness and our exploration leads to a parametrized
family of payment mechanisms which satisfy collapse-proofness. We characterize
the approximate versions of the desirable properties in cost critical and time
critical domain.
