Minimizing manipulation in matching markets without outside options

In two-sided matching markets without outside options, we compare mechanisms in terms of the number of agents who can manipulate them. Despite the existence of several stable mechanisms that are strategy-proof for one side of the market, we show that there is only one such mechanism that stable-minimizes manipulation: the deferred acceptance mechanism with the short side making proposals. Surprisingly, the Boston mechanism may have fewer manipulators than any stable mechanism. We adapt our main results to markets where only one side has outside options and to many-to-one markets without outside options.