Before revision:  We also study a design based on two-sided randomization (TSR) where both customers and listings are randomized to treatment and control , and show that appropriate choices of such designs can be unbiased in both extremes of market balance, and also yield low bias in intermediate regimes of market balance.
After revision:  We also study a design based on two-sided randomization (TSR) where both customers and listings are randomized to treatment and control . We show that appropriate choices of such designs can be unbiased in both extremes of market balance, and also yield low bias in intermediate regimes of market balance.