The conventional wisdom in finance is that competition is fierce among investors: if a group changes its behavior, others adjust their strategies such that nothing happens to prices. We estimate a demand system with flexible strategic responses for institutional investors in the US stock market. When less aggressive traders surround an investor, she adjusts by trading more aggressively. However, this strategic reaction only counteracts two-thirds of the impact of the initial change in behavior. In light of these estimates, the rise in passive investing over the last 20 years has made the demand for individual stocks 11 percent more inelastic. (JEL G11, G14, G23, G41)