  Strategic behavior in two-sided matching markets has been traditionally
studied in a "one-sided" manipulation setting where the agent who misreports is
also the intended beneficiary. Our work investigates "two-sided" manipulation
of the deferred acceptance algorithm where the misreporting agent and the
manipulator (or beneficiary) are on different sides. Specifically, we
generalize the recently proposed accomplice manipulation model (where a man
misreports on behalf of a woman) along two complementary dimensions: (a) the
two for one model, with a pair of misreporting agents (man and woman) and a
single beneficiary (the misreporting woman), and (b) the one for all model,
with one misreporting agent (man) and a coalition of beneficiaries (all women).
  Our main contribution is to develop polynomial-time algorithms for finding an
optimal manipulation in both settings. We obtain these results despite the fact
that an optimal one for all strategy fails to be inconspicuous, while it is
unclear whether an optimal two for one strategy satisfies the inconspicuousness
property. We also study the conditions under which stability of the resulting
matching is preserved. Experimentally, we show that two-sided manipulations are
more frequently available and offer better quality matches than their one-sided
counterparts.
