We extend the analysis of the theoretical interbank market model of Gale and Yorulmazer (2013) by introducing randomized trading (lotteries). In contrast to Gale and Yorulmazer, we find that fire-sale asset prices are efficient and that no liquidity hoarding occurs in equilibrium with lotteries. While Gale and Yorulmazer find that the market provides insufficient liquidity, we find that it provides too much liquidity when introducing lotteries. We also show how to decentralize the efficient lottery mechanism.