  Consider two brands that want to jointly test alternate web experiences for
their customers with an A/B test. Such collaborative tests are today enabled
using \textit{third-party cookies}, where each brand has information on the
identity of visitors to another website. With the imminent elimination of
third-party cookies, such A/B tests will become untenable. We propose a
two-stage experimental design, where the two brands only need to agree on
high-level aggregate parameters of the experiment to test the alternate
experiences. Our design respects the privacy of customers. We propose an
estimater of the Average Treatment Effect (ATE), show that it is unbiased and
theoretically compute its variance. Our demonstration describes how a marketer
for a brand can design such an experiment and analyze the results. On real and
simulated data, we show that the approach provides valid estimate of the ATE
with low variance and is robust to the proportion of visitors overlapping
across the brands.
